The only way to answer this is to find out how your existing dialer is expected to communicate with vicidial. In a way you just asked if you could use your BMW to make trips with your Volkswagen. The answer is yes: If your BMW has a trailer hitch and you can then connect the two. LOL
So: How do you want to Vicidial to generate a call through your PBX? does your PBX have a SIP interface? (If so, this may be possible.) Many proprietary phone systems/dialers have SIP interfaces, but charge a licensing fee (per channel) to use it PLUS a hardware fee for some sort of card plus installation and configuration. If it cannot speak SIP, we have a problem. LOL
If it cannot speak SIP, then we would need to determine if it has any available PRI/T1/E1 ports that could be configured to link directly to Vicidial instead. That, however, gets expensive as both Vicidial and the legacy system would require a connection card so they could talk to each other with that protocol. Which is why SIP is so cool ... it uses generic network cards for the physical connection and software (SIP in Asterisk) for the actual communication over that physical connection.
Basically: If your previous dialer/legacy system cannot speak SIP, it's not generally worth the effort/investment to keep it. Sell it while you can (if you can get $$ for it ... sell it now before it becomes worthless ...). Just my opinion, of course.
Then install a T1/E1 card in your Vicidial server to communicate with your carrier instead of your legacy system and rewire the office to allow SIP phones at the workstations (or use software phones in the agent computers) and you have just replaced the legacy system with Vicidial. And there are no more licensing costs moving forward.