A few rules which you seem to keep in mind.

your statement... "OTOH i am a bit of a valued asset and can get away with an awful lot." is a flawed belief system.  No one is irreplacable.  I know, I've been there, I've done that.

Second, tracking - if they want to get you, they will.

This is kind of an unusual request.  is the e-mail that she requests her private one?  if so, that is still not so good.  I would ask her to send an e-mail from the account in question to your e-mail.  Then you reply that you are not the party she intended to reach... that makes more sense... I get a TON of e-mail from people who have the wrong person... sometimes I do reply and try to steer them right.  not always but enough so that it would not be atypical behaviour if I did that.

hope this helps.

Texcat, my IT departments randomly check our outlook e-mails account because it has a limited capacity, but I work for a government entity so that may not apply to you.  Having said that, I NEVER was questioned because IT focused on website visits and since this account is not her or linked to a website that may be problematic, I think its ok.

This is a very good point.  "The owner" has the right to moniter use of company equipment (computers, phones).  As cut backs have happened & such, companies have become more touchy about use of their equipment (presumably on company time).  They would be totally within their rights to have monitoring software.  Even if they do not...  sooner or later the unit needs service & the IT guy sees where you've been.    
Some have used personal laptops but there's still some risk if using the company wireless.  Using a 3G devise or USB adaptor would steer clear of this totally.

I think that your idea of an incoming e-mail which you could give a prescribed reply to, is a great idea.
skb

Frankly, if it's an innocent sounding email to an innocent email address, i.e. "Thanks for loaning me the book." to [email protected], I can't imagine anything happening, with the possible exception of a reprimand for using company email to send a personal message.  If you send the email during lunch or after the work day, perhaps not even that.

Certainly I don't see how your company IT Security could link the recipient with another, no-so-innocent account.  It would take a subpeona to get all the access logs for the recipient account.

Would the MS Exchange Server log the email?  Sure.  Would anything come of it?  As you describe it, probably not.

if I accept the Professorship I am looking at (I have been self empliued for the past 4 years), this would simply be too much to ask of me.  I have needs for security as well; this would be too much for me.

Just sending an innocent e-mail to a stranger is cool.
Surfing TER would not be.
skb

use company email for the hobby.

It's a really bad idea, especially if you work for a large company.

Don't do it -- I am a Network Security Engineer. Very easily tracked from an e-mail server such as exchange

Depending on your business, simple send an email saying something to the effect of "thank you for your inquiry regarding our company's products/services.  A brochure which descries these is attached.  If you have further interest, I will be pleased to have the appropriate staff person contact you."

This is so innocent it causes no harm and poses no risk - I send these out all the time.