This is of course situational but I would say yes, it's quite possible, especially in terms of castles/fortifications which were at times very lightly defended. And when I say lightly defended, I mean very lightly defended. Even large castles could at times have peacetime garrisons of a mere handful of men. Literally just what was required to guard the gate in the daytime plus a lord and maybe a retainer or two. That might very well be it. So yes, in this context, if one is expecting some kind of shenanigans (as one usually is when the phrase "Double the guards" is uttered) it could well have made sense to increase the number of men.

Usually this worked by arming members of the household with stuff from the castle armory. I know it's not very glorious but it would realistically often mean that the cook, a few stablehands, a huntmaster, a falconeer or whatever staff you had was given a spear and made to stand guard for a few hours in addition to their usual duties. If one is expecting trouble of the more lasting kind then regular troops would be brought in, which kind depends on which type of castle we're talking about.

An interesting example of this is Oswestry Castle ín England. It's on the Welsh border, an at times troubled place. Still, between 1160 and 1165 there were a whopping 5 men stationed there. One knight, two watchmen and two porters. Doubling the guard would have meant arming the porters and bringing the garrison to a not-very-threatening five men. In 1165 Henry II campaigned against Owain Gwynedd, at this time the garrison was increased to 200 men but only for the summer. The following two years were unruly and 40 men were stationed there, supplemented for a time by an additional 60 who were supplied and paid for by the local nobility, not the king. After that the garrison was reduced further to 20 men who seems to have remained until 1174.

TL;DR - Yes, castles were often much more lightly defended in peacetime than movies portray. The scenes of guards pacing the battlements we often see in movies never happened unless the castle was besieged or under very credible threat. The walls were a daunting defense in their own right, the gate was the only place you'd expect to find men on a normal day.