choose glue carefully
Don, the answer to your question is mainly no, you cannot use PVC cement to join PVC to ABS. HOWEVER, their is a general purpose cement that can be used on PVC, ABS, and CPVC. It is made by Oatey, perhaps by other manufacturers as well. It should say right on the label that it can be used for those different types of plastic.
General purpose cement is not carried by all the big boxes and/or hardware stores, but it's not an obscure specialty item either. You may just have to look around a little.
One word of caution about the general purpose cement, it does dissolve the pipe a little more than PVC cement. With PVC cement you can insert the pipe into the coupling, give it 1/4 turn and it's done, you can walk away from it. With general purpose cement, you insert the pipe, give it 1/4 and then hold it in place for a minute or two, otherwise it might creep out on you.
Good luck with the project.