Depends on the alarm system. Mine, yes. If (when, by actual test) it sees the phone line go away (no dial tone, no active call) it issues an audible alert. Obviously it is only local - I don’t have it tied into a cell. But it does tell me something is wrong. Maybe the opening move to a break in. My move is to retrieve a firearm, knife, possibly a flashlight (TOD dependent) verify family members locations, then investigate. My move takes about 8 seconds to initiate. Me, my firearm (s), and an 80 lb very protective lab will be meeting them at whatever door or window they start coming through. They are not going to enjoy it.
If you cut my phone line, it won't send an alarm to the phone company. There would be too many false alerts to be investigated.
But, cutting the phone line does not disable a subsequent alarm. I have a cell phone backup. It's not expensive, and only adds about $10/month to monitoring.
I don't know how they would need $5,000 to repair an alarm system, unless they have a system that rivals a bank. And, I can't imagine what they have in the building that warrants spending $5,000 to protect.
Six computers can be completely replaced for that amount, and still have some left over. The data is certainly valuable (in time, not necessarily dollars), but you should have backups, stored off-site, if loss is that devastating.