I have FAX Modem "HCF 56K PCI Modem". It off-hook on third ring and receive fax OK when connected to PSTN analog lines.
But when connected to ATA186 it does not off-hook and calling party hears ringback tone indefinitely. I tested ATA186 with a physical fax an it works fine.
Yes, this should work better. In addition to modem passthrough you also will have the option of Cisco modem relay for analog ports in 12.4(4)T and above. Getting modems to work over IP can be tricky no matter what products are being used but I have had good luck with getting modems to work over the ISR gateways. Granted, I rarely see a speed above 30 kbps but at least I get a pretty reliable connection.