FoIP is possible, but not in the way you suggested - from CPU through 3CX, so the answer remains the same...No. Outbound faxing is not supported by 3CX in any configuration.
FoIP is highly dependent on a reliable and stable internet connection. As most connections are not (reliable) and even fewer are managed end-to-end, the T38 protocol was developed to try and ease some of the issues. Unfortunately, 3CX only supports T38 via the fax server extension, not on user extensions and only on inbound calls. There are some who have reported good results using the G711 pass-through codecs on user extensions, but these may use something other than the Internet (PRI perhaps) as a carrier or may have a highly controlled end-to-end connection.
Most of the ATAs support T38, but they lose this when going thru a user extension on 3CX; hence why most are used in a standalone mode. Even then, T38 requires a SIP provider who supports it and while many do, some are better than others. Almost universally, they will put in disclaimers that while they support it, they don't guarantee it.