Is it possible to connect D- and D+ to an existing USB to FTDI connection?
You can actually switch buses between ports, i.e. if you either connect the FTDI chip or your microcontroller, it'd work — just not at the same time.

What you'd avoid is having long "dead end" conductors that you either connect or not using 0 Ω bridges – these would act as capacitive load on the bus. So, keep the part of the bus that's "dead" from the host's perspective as short as possible.

You'll find that USB switch ICs exist for this very reason (and are pretty cheap, and run-time switchable!), and use very little power themselves.