Just based on a quick trial, yes it would be a significant task and I'm not sure it could be done (wrong phrase really - it CAN be done, but whether the effort required outweighs the benefit).
I adjusted the requires value, changed the settings from scsscode to configtextarea and it would install, but when you try to use it as a theme you then get errors around
undefined constant BLOCK_ADDBLOCK_POSITION_FLATNAV
and
Exception - Class 'core\output\icon_system' not found
Now it maybe that you can also backport those items, but I can't say whether those are the only things you'd come across - there's then an issue over whether the layouts/templates/renderers would match what is in 3.1 rather than the 3.2 they have been built for. Those may not throw notices and errors until you actually try to use that particular template/renderer, and maybe even then would only look strange rather than error.
Added to that, for all that effort, Boost itself is undergoing frequent updates, as is its upstream library Bootstrap4.
So I would suggest that, while it can be done (most things in software can be), it really isn't a good idea or worth the effort.
A better solution would probably be to find a good 3.1 theme (Adaptable/Essential/Pioneer are just a few out there) or persuade your client to upgrade to 3.2 - likely to be less effort involved in that persuasion than in a backport :D
Richard