You can and it sucks. Vermin trapping is slow, and they spawn faster than you can empty and replace the traps, unless you have multiple trappers. Then you need bait...
There's more than one way to handle trapping. The quote above refers to building animal traps and waiting for vermin to enter them, and that's a slow way.
Another option is to have a few animal traps made, then use your butchery workstation to capture a live land animal. Each empty trap can hold 1 vermin, and my trappers usually stay near the food storage area when they hunt, though they sometimes wander outside and occasionally seem to be trying to path to an unreachable vermin and do a zig-zag dance until I cancel the labor.
To empty the traps again, I use a single built cage and assign all the non-caged vermin into it. If possible set up a stockpile surrounding that cage that accepts only vermin types that you are catching, which makes emptying the traps super fast. If you let all the traps fill, you'll get a canceled trapping job message, alerting you that you need to empty the traps and reset the task, or you can keep an eye on the filled traps yourself.
You can keep filling that cage or alternately unbuild it and bring it (the cage, not the vermin!) to the depot for trading away. I used to do that about once a year, the cage was often worth around 1000 credit by then.
Given enough traps (5-8 is what I liked to use) and a casual eye on keeping the traps emptied as needed, I'd rate this method as 'efficient', not slow.
To quote a portion of the wiki:
Imagine, if you will, a great and grizzled mountain man with a long flowing beard and eyes shining like two great lumps of coal. Imagine this man holding a bear trap. Imagine this man chasing a mouse with this bear trap. This is the basic scenario of dwarven Trapping.
I love the image, but that's not really 'true', now is it? Cages can hold bears, (or anything, no matter how big) but animal traps can't... only vermin, no? Still though, I love the image, and would never argue with our ☼wiki☼!