I don't think the carriers in general are going to have a big issue if you sale the product over the phone and mail an annuity application. I have done a lot of telephone sales and the more complicated the product the less likely you are to close over the phone and through the mail. I have done some annuities over the phone and through the mail with existing clients. I have sold lots of term and GUL over the phone with new prospects. If you have a simple annuity. for example New York Life has a straight forward annuity and not much of an application, that has worked through the mail for me. If you have an indexed annuity or and income annuity or something with a lot of paperwork. You will have less luck getting the application back.
I have done second annuity sales with clients over the phone. I keep it simple brief explination fill out the app over the phone and mail with stickies for signatures.