Does OpenMPT have a sample generator like MilkyTracker?
No, but it's on the roadmap. https://bugs.openmpt.org/view.php?id=50
Don't forget the OPL synth. Yes, not a true generator, but you could create a sound and convert to wav that way, or just use that sound in your song. .s3m files can be distributed with the OPL synth instruments in place if you want to have compatibility with other programs and not use the mptm format. In that case you are limited in how many instruments you can use as OPL2.0 only allows for 9 instruments at the same time.
I've added an example tune that showcases this.
In the Samples editor, you can "draw" your own sample using the "Toggle Sample Drawing" button.
It's a pen icon next to the zoom icons. It's a rough approach, but it is there.
Here are some other freewares you might find interesting:-
https://www.nutty.ca/?p=180
http://labbed.net/software/labchirp/
https://raylibtech.itch.io/rfxgen
https://www.bfxr.net/