yes, its possible, just not as easy. If its a very light, short knife, but with good edge geometry, it can do OK- i cut a lot of smaller trees back in the day with an old hickory 7" butcher knife. I have a 7 1/2" hudsons bay knife i made years ago that chops pretty well for its size, but weight as much as the 10 1/2" bowies i make. .
I prefer a larger knife, though. Once you get into a 10" or so knife with good geometry and weight distribution, you have got a real tool for wood up to the 5-6" range. Leverage, baby. But i dont chop much firewood, i just break it.
I chop and carve when i make traps, shelters, tools, ect, but life is too short to chop every stick of firewood. I will trim trails and such with it, though as it carries lighter than an axe, and is handier for me than a hatchet or saw.