If aliens decided to use our resources, they would probably do something like build a Dyson Sphere around the sun, which would mean there would be nothing left for us. It wouldn't matter how big they were, because they would use the resources we need. Look at it this way - we don't notice or mind the presence of insects or flowers, but that doesn't help them when we pave or plow their habitats. A lot of wild things escape us because we aren't that good at harvesting every possible resource, so there's a lot left over, but presumably aliens would be more efficient.
Because of the properties of exponential growth, there would be nothing left over for us. If two organisms double their numbers 250 times, their numbers would roughly equal the number of atoms in the observable universe, which means there would be none left for anyone else.
The only hope would be that they either don't reproduce, which seems unlikely since they would be the survivors of a process of Darwinian evolution just like any other critter, or that they're Space Vegans with a moral code against exterminating other species. We really don't know how they would think.
