When I wrote my answer I was young and stupid. I've since matured and would like to state:
most of what I've written below is nonsense. Your sentence "fishermen trawled at least 100 kg of fish" is fine. It's not very natural, but it's fine.
Anyway, original answer:
No, it doesn't really make sense, as "to trawl" generally describes the process of fishing, rather than actually catching the fish.
You can't trawl a fish but you can trawl for fish.
So I'm afraid you'd have to say something along the lines of:
The fishermen caught more fish than they'd ever caught before during that time of year.
You can use trawler (as a noun) to describe the boat, so you could also say:
The trawlers pulled in at least 100kg of fish
where "pulled in" is a colloquial way of saying "caught."
I thought I'd correct your second sentence's grammar (your first sentence is fine):
Fishermen trawled an amount of fish that they have never before at this time of year.
You need a verb between "never" and "before," and if you're mentioning a previous date you need to say "that time of year" instead of "this time of year." ('This time of year' is too ambiguous, it would generally refer to the time of year it was when you wrote this sentence.)
Fishermen trawled an amount of fish that they have never trawled before at that time of year.