bad idea for an experiment:

take a betamax tape, and a vhs tape. open both casettes, remove the actual tape, and put the beta tape into the VHS cassette.

First of all, it won't play. obviously.
but then see if we can record to it and play it back.

dooo dooo doo dooo....
I'm in. (to the Beta tape)
and I'm into the VHS tape
cross-winding the tape
where's a VHS rewinder when you need one?

why VHS beat Beta in one, oversimplified example:

The reel on the right is beta. the reel on the left is VHS. A bigger reel meets it holds more tape. More tape means it can record for more minutes.

Beta tape is now wound onto the the VHS reel.
Now I need to unwind the other reel of the VHS tape and splice it back together

how do you unspool half a kilometer of tape?

a power drill, obviously!

okay, tape is back together. Now I'm going to manually rewind it, because I don't want to risk my VCR slamming into the end of the tape at high speed.
I should 3D print a VHS-reel-to-drill adapter
PRINT IT
still printing but I finished rewindng it by hand
and it's back together. time to go see what the VCR does.

and it gave a signal! it's gibberish, of course, but I'm amazed. I thought the VCR would just stop or show nothing.

So this is what happens if you play a Beta tape on a VHS VCR: gibberish lines.

I am currently recording a video onto the Beta-VHS tape. You can probably guess what video.
Here's a GIF of what it looks like in action

And here we go! So the answer is: YES.

You can absolutely record VHS signals onto Beta tape.

(The pause at the beginning is just me not starting the blu-ray player at the same time as I hit record on my VCR)

@foone Would have been much more surprised if tape from a Beta cartridge wound into a VHS cartridge wouldn't work. They're both just 1/2" videotape. The tape had to be durable enough for auto-loading into the transport and helical scanning, so sauce for the goose is sauce for the gander. Ampex figured that much out in the 1960s.