Absolutely. What the center would do is, after importing a night's scores, they would back up the league into a single file, which you could take home, restore from that backup, and do whatever you would normally do.
Do note that if you do any changes to lineup orders, add/remove bowlers, update bowler information, etc. you should back up your league to that single file, and take that to the center, where they would restore from your modified backup before they open the league and export information to the scoring units.
If the center doesn't upgrade to BLS-2018 next season, while you would be able to take a backup home and open it with BLS-2018 that you would have at home, the center won't be able to work with your modified backup because once opened with a newer season's software, it won't be readable by older software. If this becomes the case, you could do any printing and uploading at home, but any roster changes would need to be made at the center's computer to reflect any changes that you might do at home.
Always check, download, and install the most recent update of your software to ensure that issues may have been corrected.