Sure it can...like you can find "love" with a stranger you meet on a train...or a waitress at the place you have breakfast, or run into your high school sweetheart 20 years later...it is possible...more important question is:
Is it probable?

I would say the probability of any given client winning the heart of any given lady after one, or many, paid appointments is not the best.

Then of course if a relationship does happen, comes all the issues of "how you met", can you handle what she did or still does to earn a living, what happens when you discover that she is a woman first and with that comes all the things that happen in any girlfriend relationship,  when the time together isn't just all about you because you are no longer paying for it to be all about you...

Then there can be a certain "weirdness" with the fact that any relationship was done, for a lack of a better word, "backwards"...you meet get physically intimate without knowing much of anything about each other...how do you turn back the clock on that? How do you go from paid encounters to non-business relationship? Do you stop having encounters and just date like had you met any other way until that personal relationship reaches a point where intimacy is appropriate?  Do you date like in any other relationship but if the time isn't right for physical intimacy in that relationship then steal off together where you then still pay her for that encounter?  If you would expect her to stop working do you pay her what she would have earned?  and if so does that make you her SO or her exclusive client?

If you are going into the "hobby" thinking you will find a girlfriend better to go to something like match.com where the women are looking for boyfriends and relationships than to try and find that with the ladies here.  

The fact that many ladies in this business already have SOs and meaningful relationships doesn't help with a quest to find Miss Right by hiring her either.  

Then comes the question of if you did enter the hobby with hopes of finding a girlfriend why do you think you want to specifically date a woman in this business?  To get for free what others pay for?  Because you think a SO relationship will be like a session?  Because you think she will be sexually voracious at all times?  Because you think with a lady in this business relationships won't follow the patterns that happen with other women such as less frequency of sex etc?

If so....I wouldn't count on any of those things being true.  

Can it happen? Sure.  Will you be the one client out of many that she has some special connection with?  That could happen too.  Can you handle it if it were to happen?  That only you know the answer to.

My best advice, don't go looking for love in the "hobby".  If it happens, great;  if it doesn't, great because that wasn't what you came for anyway.  If it is what you started "hobbying" for, then you are most likely setting yourself up for a great deal of heartache as you try and fall for and win the heart of each lady you see as if it were an audition for a boyfriend position instead of a business arrangement.

Now, after all that I guess I should ask do you just want to find "love" with any lady in this business or do you have a specific lady that you are having feelings for?  
If it is just any lady in the business remember, this is what she does not who she is, and just like not all accountants, cashiers, doctors, etc are alike neither are all ladies in this business.
If it is a specific lady that you are having feelings for, then talk to her and not random strangers on a message board as she knows what she does and doesn't feel for you, we here do not.

Quite a while back on my first and only time with a certain unattached provider, she told me that the only guys she considered potential SO material were her customers. She said none of the civilian guys she dated could handle what she did for a living even if she was willing to quit. She refused to try and hide it from them either.
  After telling me all about her personal life and living situation, she suggested that for our next date we go out to a movie. I have to admit that freaked me out a little at the time. I never did call her again. I feel bad about that now.

There is a major difference between being "friends" with a provider and being a boyfriend of the provider.

I have no illusions that I am any provider's boyfriend.  OTOH, I do believe that I am a friend of at least a few of the beautiful women I see.

I have become

very good friends with one provider.  After I saw her, I tutored her daughter in math, and somewhere along the line we found a connection from over 20 years ago.  No romance here, but a good friendship evolved.

Swim

But, IMHO, it's impossible to 'make' that happen. If it does happen, it will be a bit of serendipity for which you can be very thankful. In my experience, it's taken quite a bit of work and some real skills at building relationships (on both our parts) to construct a relationship that is meaningful for both of us. It's a unique relationship, too, completely unlike anything I've experienced before. We know each other in ways that are totally different from the way anyoen else knows us.  Worth every bit of investment on my part so far.

Does this happen often? It appears not although a few hobbyists seem to have managed it. It also seems that those hobbyists are generally more mature and have learned a bit about what's important in life and what's not.