If there's only a small number of them there's probably little measurable impact--yet.  When there's a huge number sweeping an area to consume everything in their path, they're literally taking the food out of the beaks of smaller native ground birds like grouse (4 species) and ptarmigan (3 species).

Does EVERY invasive species destabilize naturally-occurring ecological systems?  Perhaps not--if you're willing to ignore the risk of introducing novel or unknown pathogens with them.  But more often they do.  About 1900 someone thought it was a good idea to introduce 'ornamental' Japanese chestnut trees to Ohio.  The chestnut blight (Cryptophonetrica parasitica) that came with them destroyed 75% of the forests of eastern North America.  They weren't cut down to build 'little houses on the prairie'.  They were wasted by disease.

The American chestnut is nearly extinct--botanists struggle to keep alive a pitiful remnant (~100 saplings) in Canada growing from the stumps of vanished groves.