Yes, but that trap adapter is the thing that has to match the existing piping.
While they do make multi-purpose (clear/amber colored) cements, they are not specifically for transitions. Transition cement is a god-awful green color, and hard to come by.
Codes differ everwhere. ND will allow one ABS/PVC glued transition, but only at the building drain/building sewer connection. MN requires a mechanical transition--female to male adapter, but most locales have begun to accept shielded mission bands for the transitions (since the orange sticker now states plastic to plastic).
All I know is that if I was to have any inspector around these parts see a PVC trap adapter glued onto an ABS pipe, I'd have alot of explaining to do, and I'd better have the saw ready.
Whether or not it will work is not for me to argue, or to give credence to. I'm supposed to know better.