Yes, base salary always counts against the cap (as well as any roster bonus paid in that year)
Basically cap number = base salary + roster bonus + pro-rated signing bonus. Which is why guys who have big base salary jumps and/or roster bonuses, who are several years into their contracts are prime targets for cuts/renegotiations of their contracts.
When a player is cut/traded, the remaining pro-rated signing bonus is immediately accelerated and counts against the cap as "Dead" money (money that counts against the cap, to player who aren't on your roster)
Its a bit more complicated than that (you can now spread out the dead money cap hit over two years, for instance), but theres no way to hide base salary beyond renegotiating the contract and converting base salary to signing bonus. The cap hit is still accelerated, but if the player is on the tail end of their contract this usually doesn't amount to as much as if you paid them their base salary (for some reason, salaries nowadays are quite often heavily backloaded). Players usually don't mind this as long as they get the same amount of guaranteed money (i.e., signing bonus and that years base salary/roster bonus), or they think that they're not going to earn more the open market (Will Smith would not)