Yeah, that works for middling rolls. On very high or very low rolls, though, they pretty much know.
And it can be argued that that's ok. You roll a nat 1 on the forgery and the DM says, "Yeah, that's just not in your ability" or whatever.
But I don't find a dead-end plan as interesting as something with high stakes and tension.
I know (I know I know I know) that RPGs aren't movies or novels. But can you imagine a WWII spy movie scene where the good guys try to forge a passport, but they can't do it, so they just move on to plan B? I mean maybe if they squandered all their time doing it, and now there's no time for plan B. But wasted time counts as a meaningful consequence. In the absence of that, why waste precious screen minutes on such a thing? I feel the same way about table time.