If you run your knobbies at typical MTB pressures, and you run your slicks at higher pressures, you should experience less rolling resistance, which could translate to higher speed.
I don't know what tires you're talking about exactly, so it's hard to say how much of a difference it will make. I run some pretty aggressive knobbies on my MTB (Panaracer Fire XC Pros) and with <35 PSI in them, that makes for some noticeable rolling resistance. On my vintage no-suspension MTB, I run slicks with 60-65 PSI in them, and those are halfway to being road-bike-like. Even with the MTB gearing, I can hold 15-16 mph on that bike for a decent amount of time.
You did not indicate what kind of suspension your MTB has. With any suspension, you're probably going to get a little pedal bob, which will rob you of some energy. That, combined with the upright riding position, will hold you back a little. But the engine (your strength) is more of a factor than tires, suspension, and bike weight.
Once upon a time a friend of mine-- road bike rider, likes Italian bikes, pretty fit at the time-- used to regularly get passed on a local muni trail by this little guy on a vintage mountain bike who was dressed in street clothes and riding to/from work. These roadies would be doing a paceline at a good speed, and the little guy on the mountain bike would just roll right past them, comfortably holding 2-3 mph faster. I wasn't there, so I can't tell you if the mountain bike guy had modified his bike or what. But he used to say "good morning" or something similar, every time he passed them, with a big smile.