I've done it before. They shouldn't be offended, since they'll charge the same whether you use their proucts or theirs (saves them money!). Just let her know that the products she usually used don't hold until you get home, so you thought you'd bring your own.
Sometimes I apply and sometimes they do, depends on the stylist. But I've often brought my own products.
SF Bay Area, CA * "The Angel-Goddess-Guru of Haircoloring" 3b/c/a mix. medium texture, low porosity
My Motto: Strand Test! some hair pics
-- gone, but never forgotten.
I've always asked first if they minded if I brought my own and I haven't had a stylist yet object to it. In fact, one time I brought a product in that the stylist had never used before and liked it so much she started carrying it in the salon and using it on her own hair.
I don't see a problem with it. Especially if I was comfortable with the stylist. Since I don't have one of those yet (well, I have in the past, just not currently), I just forgo the wash (I do it at home beforehand) and don't bother with the dry/style afterward. Saves a couple bucks too.
At first I worried that I wouldn't be able to tell totally how I felt about the cut if they didn't style it. Then I realized that I couldn't tell from their styling either so I go home, do it myself, and most stylists don't have a problem with you coming back for a little tweak once you see what it does.