No, don't think so. A tailwheel is identified as an aircraft variant that requires differences training and sign-off by a qualified instructor. Until that time you cannot act as PIC on such an aircraft, not even just in the air (with your buddy acting as PIC for take-off and landing).
If your buddy is a tailwheel FI (or CRI, possibly?), then you can log Pu/t while he logs P1. Otherwise, I fear your logbook has to stay empty.
I've been in the exact same situation where a friend (who has a tailwheel endorsement) asked me to go for a ride in a Cup a month or two ago. Very interesting, loads of fun, but I've got nothing to show for it in my logbook.