Would this be inappropriate?

i dont see why it would be bad

 

I don't think it's inappropriate. Go for it! The worst that can happen is that you'd get a, "No.".

 

Bad, of course not, but you'll quickly realize that schools don't care about how many hours you've shadowed. You won't get an great rec from someone you shadow only because you're not actually doing much, only well, watching. Do it, if you want to learn about being a doctor, but nothing more

 

Do it. People come on SDN all the time asking how they can find a doctor to shadow. The small connection you described is pretty much what you need to get your foot in the door.

As far as a LOR, don't hold your breath. If you shadow the doc for a long time (multiple weeks) and develop a good bond with them, then you could justifiably ask for a letter. Most of the time though, shadowing can be a little too superficial for docs to base a good LOR on.