As the title says. I want to say "no", because Aligned Class is already really powerful, but it comes down to whether the favored class bonus is a "class feature" or not.
I wanna say no because Favored class bonuses are gained once gaining a level in that class. This prc isn't giving you the experience to gain extra levels in the base class, it's simply allowing you to treat its level as base class levels for the purpose of what class features you gain. Since you're not actually gaining levels in that class through experience, I'd say you wouldn't gain the favored bonuses of that class until you put another level into said base class.
Seens like a fairly straight forward no to me.