Do naturally spawned animals affect the limit of animals I spawn from spawn eggs?

Solution 1:

The use of spawn eggs ignores most of the checks for whether something should be able to spawn somewhere. In particular, no check is made for amount of mobs already spawned. You can use spawn eggs to create hundreds, thousands, or even millions of mobs in an area; the only limit will be the processing power and memory needed to handle them.

Solution 2:

There is no mention of the spawn limit on the Spawn Egg page, and no mention of a Spawn Egg failing to create the desired mob (due to that limit).

Additionally, I know from experience (and online images) that it is possible to create vast farms (that would override the maximum for passive creatures).

Thus, your spawn eggs should perform as expected.