Firmware updates

I work with 2 MacBook Pro's one that does the 32bit Mac OS and the other the 64bit Mac OS,(+their version BMD software) because i still use some 32bit software that hasn't an update for the 64bit OS.
I have some BMD hardware: Atem Mini, Video Assist monitor5'(3G) and the Intensity Shuttle (ThunderBolt2)
Now my question is, when i update the firmware of these devices with the 64bit supporting software,
Can i still use these devices with my MacBookPro that uses the 32bit software (drivers) ?

every mac book pro from 2007 and up has 64bit kernel

32bit software run up to mojave
with catalina and big sur all software must be 64bit

blackmagic software is 64bit since years

the only difference with your books is the system
so you have a look which minimun system is recommended by your BMD software

Thank you for your reply !
So, with updating the firmware of the BMD hardware on my 64bit OS (Catalina) will have no negative effect on using the BMD hardware with my MacBookPro still running on the Sierra OS ?
Using computers, hardware and software has made me a bit suspicious, to expect the unsuspected....

if the software runs at sierra, there will no problem