scyue, in general the answer is yes. "Sounding closer" or "sounding farther away" depends on a number of things, but the main one is the amount of direct sound energy being picked up, as compared with the amount of sound energy that has bounced off of the floor, ceiling, walls, people, other solid objects any number of times before reaching the microphone.
The ear/brain can nearly always tell the difference because (a) the path lengths for reflected sound are longer, so the reflected sound energy arrives after the direct sound energy, and (b) the process of reflecting sound generally reduces its high-frequency content, so most reflected sound isn't normally as bright or brilliant as the direct sound.
Since cardioid microphones suppress sound from behind them, if they're aimed at the sound sources, they will pick up a greater proportion of direct sound than an omni at the same distance would do. There's even a number called the "distance factor" which says that in general, a cardioid placed about 1.7 times as far from a sound source as an omni will pick up about the same proportion of direct sound vs. reflected sound.
That calculation depends on some acoustical conditions that don't always hold true in real life, so the 1.7 figure should be taken with a fair-sized grain of salt. And of course once you get far enough away from the sound source, all bets are off. If the direct sound amounts to only 10% of what your mikes are picking up at a given distance, increasing that to 17% won't really help. But for close-to-medium-distance miking, the "distance factor" is generally more or less valid, and should answer your question, I think.
--best regards