Yes there is a limit. The limit is determined by the base production value, and caps at either 2040 or 2295 per month (or 2550 if on a forest map, due to 10 production ticks instead of 8 or 9). This also depends on you having smooth economy enabled.
To quote a TTDPatch developer on the OpenTTD Forum:
"The base value for production is the amount the industry produces in
one step. Since a primary industry produces cargo 8 or 9 times a
month, the monthly production is 8 or 9 times this base value. For
example, the base value for a coal mine is 15 tons, so the monthly
production is 120 or 135 tons. This base value is capped at 255, so
the maximum possible monthly production for any industry is 2040 or
You could always look through the source if you don't believe the forum post. I'll even narrow it down to the file I think it would be in for you. Good luck!
I'm not entirely sure about the output of secondary and tertiary industries. In my experience their output is determined by input.