It depends on the drawing operations that you perform.
It also depends on whether the operations you perform can be hardware-accelerated by OpenGL and whether that acceleration is beneficial. (On OpenGL, it can also depend on how you perform those operations, since some drawing methods are known to be measurably slower than others.)
If you want to know for sure, then write some simple programs where one draws with Allegro's un-accelerated API, then another which draws with equivalent OpenGL operations, and profile them.
(By and large, I think your results may be meaningless, if your program is too simple or relies on operations that are too simple. Many drawing operations are so quick that even with hardware acceleration, you might not see any difference, or the difference may be so small that it won't matter.)