I've been throwing in push presses into my routine lately (mainly because I've been starting out with a weight too heavy to military press). Are there any disadvantages to keeping push presses in my routine over military presses?

Likely,

MP + PP at the same time = boost on the MP
PP without MP = some drop on the MP

It can also depend on how you're training the PP -- as an assistance for the MP or for the jerk. You'll see less of a drop if you're using as little leg drive as needed (i.e. assistance for the press), but you'll see more of a drop if you're not too particular about the amount of leg drive used (i.e. assistance for the jerk).