There is no problem connecting two OBi devices to the same Internet router. However, I see a few possible issues:
Foremost is emergency calling. Google Voice does not offer 911 service. You can configure the OBi with a secondary provider, e.g. Callcentric or Anveo, which would be used for 911 and also serve as a backup. However, the system will still be less reliable than a landline; a failure of power, equipment, Internet service or provider will prevent it from working. Possibly, you will want to keep one basic measured landline. The OBi110 can be configured so 911 calls would use the landline; in a power failure, the phones would be automatically connected directly to the landline.
In your existing system, although the two lines have different numbers, they may be set up for hunting, sometimes called "in rotary", which means that if the main published number is busy, an incoming call rings the second line. If you have that feature and want to keep it with the new system, be aware that GV does not offer hunting. It's possible to configure two OBi devices to do that, but I'm not sure that it would be friendly to your existing phones.
A few multiline phones have hum or noise when connected to two different VoIP devices. There may be no easy way to tell whether your models will have this trouble, or whether it would be loud enough to be objectionable, other than trying it.
I would not trust my business to Google Voice. Although it's a very reliable service, there is essentially no support, so if something did go wrong it could take a long time to get it resolved. I'd seriously consider a quality paid provider -- you can still achieve considerable savings over CenturyLink.