Chan SIP won’t do that - Chan PJSIP will - That’s a weird setup though.
We help a national program here in Albuquerque, and they are using Telos but they are still using Analog Handoff’s from the Asterisk to the switchboard.
If the Telos is expecting ringing on all the lines at once then fine - my guess is that would show ALL the lines lit up at the same time, and until you answered and secured the caller, you would not see any other callers.
PM me is you need more info - but I would talk to them.
Either way, the processing overhead on the PBX is minimal - making any combination of things ring is not CPU intensive.