Yes, I have. Only temporarily, and only to test some VOIP phones we bought to see how good they were.
It’s fairly straight forward. Build a PRI between the two systems, and use UDP to send your extensions to the PRI. Asterisk takes it from there.
There will be different features that don’t translate well, or work at all. Like display data may only work in one direction, (or not at all). Voicemail messages between senders/receivers on different systems can’t be replied to. Asterisk voicemail messages can’t be marked urgent. CDR data is created on two systems now. Your call about the importance of such things.
As far as replacing a system with Asterisk; That’s a tall order. A G3R is a big machine. A good Asterisk box is generally maxed out when it supports 50 or so lines. You’ll need a farm of servers to support the number of lines/trunks with Asterisk that a G3R can. It can be done, but it’s a big replacement.
Some G3R features Asterisk won’t have, or will simulate, or will have to be developed by you. Shared line appearances is new, and doesn’t work on ALL phones. Terminating extension groups don’t exist, but can be simulated. Coverage paths are easy to do with macros but harder if you have a lot of custom coverage paths. (you get the picture)
You suddenly acquire all the maintenance needs of your network services too. Server updates, replacements, backups, etc… All have to be done. Even the phones will need periodic firmware updates.
Each asterisk box, and phone becomes an individual IP address node on your network. Be sure your sub-nets are configured to support that many IP addresses. Will you need to re-wire your building(s)? VOIP uses Ethernet, (and ideally Power Over Ethernet) your current phone station wiring may not be up to snuff. And of course, you need good strong network switches with a proper amount of backbone bandwidth.
And finally, there’s support… You’re it. There’s generally no one you can call to fix your system if it fails. Days, nights, weekends, holidays, etc… you’re the go-to guy. Be sure to factor in the ability of your businesses to tolerate down time while you maintain/repair the system, and your own ability to provide all the maintenance for it.