I also don't think studying algebra helps you directly with programming language theory. However algebra is of indirect help if you want to learn category theory, because the latter is a direct generalisation of the former. It is rather difficult for a non-mathematician to pick up category theory from scratch without having first seen the the algebra that category theory abstracts from. Universal properties, category theory's most important concept, appears bizarre and disconnected from reality, unless you have seen it working in the much simpler settings of groups, rings, modules etc.

To that caveat, I'd like to add that neither Rotman nor Birkhoff/MacLane are ideal places to start learning algebra. There are plenty of gentler, more modern books. In terms of tomes that are available online, I can recommend Shoup's "A Computational Introduction to Number Theory and Algebra" [1].

As an aside, note that category theory is used only in the part of programming language research that is about (pure) functional programming. In other sub-fields (e.g. OO, logic programming and concurrency), category theory has not so far proven terribly useful.

[1] http://shoup.net/ntb/