It depends on which formats that hardware is capable of recording to. PP can work with a LOT of professional/common camera formats, but with web and other Internet videos, you take your chances. Some work and some don't. Best bet is to know about codecs and formats, and run some tests.
The delay will be considerable, meaning you won't be able to edit in PP until after the web cast is over, and you'll have to export the whole thing to a new file before it can be recast.