If you use selective push to only push the files, it will work fine, regardless of the type of multisite network. If you push just the database or the database and files, it may or may not work, depending on how your multisite is set up:
If it’s a subdirectory multisite (example.com, example.com/subsite1, example.com/subsite2), push to live will work as expected.
If it’s a subdomain multisite (example.com, subsite1.example.com, subsite2.example.com), it will work fine, provided the subsites don’t require HTTPS.
If it’s a domain-mapped multisite (loads different subsites at completely different domains, e.g., example.com, example1.com, example2.com), it won’t work without significant manual setup.
Option 1: Turn off domain mapping and go back to the standard subdirectory/subdomain setup. Do a search and replace in the database manually.
Option 2: Set up staging subdomains for each live domain, add all those to the staging site, and run a search and replace in the database manually to update each domain after pushing staging to live.