No. Combat-time skill/ability checks don't necessarily require a PC's action.
[Sources reviewed: PHB, DMG, Sage Advice (the one that matters)]
This is because there's nothing about combat-time that changes the fundamental concept of a skill/ability check:
- player declares action+intent;
- GM decides whether the action is guaranteed, impossible, or requires a check (DMG p.237);
But in combat we've got to track actions, so there's an unstated--but necessary--step 3:
- GM adjudicates the action-economy "cost" of the declared action. (See "Other Activity on Your Turn," PHB p.190)
It's simply not impossible for a player to declare an action that's (a) interesting to roll a check for, and (b) the GM rules shouldn't consume an action during their turn.
But in my experience, GMs have required an action every time. Why?
I've been subjected to this as a player, and I believe I've done this as a GM. In my case, it's informed by the Hide and Search actions described in the combat chapter. They clearly set the precedent for "you want to use a skill above-and-beyond passive use? You've got to devote some time and attention to it, as represented by your action."
There are some examples where we will not require a check, by the rules: see Grappling and Shoving (PHB p.195).
But there are plenty of examples where we might "charge" an action: swimming during combat might just be part of your movement or it might require an athletics check (PHB p.182), and it might be so strenuous that a GM feels it should consume one's action. Likewise if one tries to Intimidate the rushing mob, I know many GMs (myself included) who'd require enough in-game effort/attention go into that display that it consume one's action. The payoff, after all, is pretty high!