Short, realistic version is No. The way language works is that each person builds their own version based on what they hear around them. So aliens with no verbal interaction have no input whatsoever. The only way for them to get input would be through direct, verbal interaction. Written interaction would be less effective, but still might add a couple vocabulary words.
Let's say that the aliens can disguise themselves as humans for the purpose of getting that direct input. They'll still have a steep, uphill battle.
I was going to write about how I'd go about subtly influencing language in a particular direction as an outsider having extensive contact with native speakers, and I'm coming up completely blank on a practical method. So here's something seriously impractical.
Children learn language primarily from peers, parents, and any other adults they spend significant time with between the ages of 2 and 5. By the time a kid is kindergarten age, most of their internal grammar is fixed, and they use grammar nearly identical to the adults around them.
So the best I can come up with is for the aliens to have a HUGE hidden presence on earth, to the point where every child can expect to interact with several of these aliens in a close manner (pre-school teacher, frequent babysitter, or similar). And these aliens use slightly different language and grammar. Some of the kids would pick up on some of the different speech patterns, and add a few to their native language. Theoretically, this could be done over many, many generations, subtly influencing the language by exposing it to a foreign input. The hidden aliens could slowly change their own language usage over generations to be more and more similar to the alien native tongue. This would be an unreliable method, involving a ludicrous amount of dedication and time on the part of the aliens, and in the end, the result would probably not be what they wanted. This has never been tested, for obvious reasons.
But really, by the time you've got a few million hidden aliens among the human population, why not just teach the alien language in schools? It'd be cheaper and easier, and if it was economically beneficial, it could easily become widely used, much like English is today. Or go the pure sci-fi route, and use telepathy beams to teach language