Yes, but it should take no more than 1-2 hours, and require no parts. It's obviously a one-time charge.
I don't really know your panel that well - it's possible they won't have to reprogram at all, and can just reset the engineer codes to gain access to the menus and turn off the communicator.
But to be fair you are still looking at a minimum charge, so won't make much difference to the cost. It's not 'their' data they will be putting in, just setting up the system, again as if it were only just taken out the box.
The alarm will either refuse to set and/or make a tone / chirp / chime every now and then to alert you to a cut phone line. I wouldn't do it, if you can get someone in within the week then I would just live with an extra week or two's phone bill.
I don't do 'digi' (telephone line) monitoring, but would suggest quite cheap though depends on what other 'services' you do or don't get for that fee.