Accepted answer: no
It's customary to send off a worker early in the game to scout the enemy's base. I do it, too, but find the information gained to be of not much use, at least in the lower leauges.
I usually can only see their first non-supply building, and whether they got gas, before they wall off (P,T) or get zerglings. Against Protoss I can often see if they have a cybernetics core or a forge, Terrans often sometimes wall off before I get there at all on larger maps.
Now, the vespene info should be useful, but unfortunately I've fallen to bronze leauge (haven't played in a long time and switched from Terran to Protoss), and on this level people often don't seem to have a bigger plan.
The only thing I can consistently see when scouting is whether they are preparing some kind of cheese, placing a pylon or a rax in front of my base etc.. Against most other forms of early aggression I can easily defend myself with a variant of the FFE, just by walling in at my main or natural (depending on the map).
So, I've been thinking it's kind of a waste to send out my probe, and I'd have an economic edge if I don't. If I keep it at home, that's ~50 minerals a minute, plus the 50 minerals of the probe. That means by the time I have a gateway, I can afford an additional zealot, and never have to stop producing workers.
Obviously, that's not what people do. So would that be a good strategy, or where's my mistake?