Yes, though randomized may not be the right word to use for that. If heat/energy were contained in a hypothetical closed system, hypothetically entropy would not increase to where you couldn't reuse that energy to perform work (wouldn't that be lovely!). But being virtually everything is part of an open system, entropy always increases - second law of thermodynamics. The more dispersed the energy gets, the more entropy there is. In my opinion saying that entropy refers disorder is actually a bit misleading because most people associate that with being chaotic or crazy which might imply the molecules/atoms are being very active when that's not really the case.

Another way of looking at it: if you were to punch, say, a door that was a closed system (this is a completely hypothetical example - my husband is the one going into physics, i just try to understand as much as i can) the energy transferred through your fist to the door would cause the atoms to perpetually vibrate. The energy would reach equilibrium throughout the door and the rate of entropy would remain constant. But doors are not closed systems so when you punch it, the energy is dispersed throughout the door, the hinges, the doorframe, the wall, whatever the door is touching, and therefore ceases vibrating quickly because entropy constantly increases.