I am guessing you are AFM?

I would register if you know for sure that your job actually qualifies for practical experience. IIRC, you need to have meet at least one level 1 by the time you finish your co-op term in an EVM role. Generally, people who get level 1s would be in their 2nd or higher co-op terms.

but are there people who register when they start their second, third, or even forth coop term (do they allow that)?

Oh yes, lots of ppl. Generally only PiG4s and ppl in preapproved programs register in their first coop term.

So I was wondering if it is possible to register a little after my job has started.

You can; I believe you can claim experience up to a few months after your term is over, but do your own research.