Providing phone line current for direct modem-modem communication
There is no issue with using a battery (or low-noise, isolated power supply) in series with the 600Ω resistor (and capacitor to bypass audio frequencies), as long as the circuits are otherwise isolated (i.e., there is no common ground). After all, the original specifications for POTS (Plain Old telephone Service) was 600Ω impedance (and 48 VDC open-circuit voltage) in most countries, and power was supplied through banks of wet cells (lead acid batteries).
A ringer signal of ~100 VAC, 20 to 40 Hz (&quot;cycles per second&quot; in older documents) was used, and the phone bell had a capacitor to resonate at the particular frequency, so only one phone would ring on a shared &quot;party&quot; line.
If either (or both) of the modems have internal transformers on the phone line, then the resistor/battery/capacitor supply will work, with some caveats.

9 VDC might be insufficient; you might need to snap three or four 9-volt batteries in series. Test and see.
There is no ringer voltage, so your modems might need to be manually taken &quot;off hook&quot;, i.e., turned on.
Batteries will only last a few hours in use.

If there is no transformer isolation, then you'll need a 600Ω:600Ω audio transformer, and batteries on both sides of the transformer.
This worked well to connect older computers, such as two Atari 800 XL's, through 1,200 bps or slower modems. Ah, for the old days of wooden bread boards and bailing-wire connections...
That said, you can buy telephone subscriber-line interfaces, if you have a long-term need.