First off my understanding is that transmitting facsimile documents over SIP trunking produces "unpredictable results."

So I would install at least 2 POTS lines. You need the one you are considering for the fax service and possiply one to route the call on to the main office. However what I think you are considering may, in fact, have a better solution.
You should really have more POTS lines as backups. Also you have E911 to consider.
Setting the E911 issue aside, I can think of at least two ways to proceed depending on the equipment you currently have or plan to have on site. So let's start with a few questions:

- How is the branch office physical layer configured?
- Are you using Digital, IP, or SIP desksets?
- Do you have a local survivable processor (LSP)?
- If no LSP, are you considering installing a G450 Gateway, LSP and Analog board? ($$)
- Do you receive calls from a local trunk or from a data link to the main office.
- How close are the two buildings? Same state? Same campus? different state?
- Am I correct that you had a fax machine in the branch office and now want to send inbound transmissions to a fax server in the main office?
- Is your email handled by an Exchange or Lotus Notes server?
- Is that server in the main office?
- Did you initially have a fax machine in the "branch office?"
- Is there currently a fax number "assigned" to the branch office?
I believe I can give you a leg up once I have these answers.