> Is there a DAC only mode in the RME ADI 2 DAC which shuts down the amplifier unit
> and just acts as a DAC for the XLR outputs

Its a preamp and without a preamp you would not get any signal out.
The volume poti gives you the possibility to dial in the level that you want.
You can turn autoreflevel off and select a suitable reference level for the outputs and then set the volume up to 0 dB.

But .. are you aware of, that the SMSL SP200 doesn't bring you any benefits in terms of better sound ?

1. D/A conversion is already being done at the ADI-2 DAC with its SNR/THD values

2. adding additional devices in the "analog domain" (adding more circuits) won't make the sound any better

If the purpose is only to support balanced phone mode ..
Is this required by your phones ? Or do you think it would make the sound better ?

3. balanced mode brings maybe a few dBA SNR more, but which is questionable because not audible
    most phones like ie Audece LCD-3 have anyway separate cabling from the plug at the ADI-2 DAC to the
    two drivers on your phone. More is really not required.

If you want to spend a few bucks more for balanced operation, then I suggest to upgrade to the ADI-2 Pro FS R BE.
Then you have all in one box and more ...
- new AKM DAC chip with one additional D/A filter
- 2nd independend amplifier to support either 2 phones or balanced operation for 1 phone
- the new remote
- A/D converter which allows you to digitize analog audio material if you have
- Besides ADAT/SPDIF input also an output and features like dynamic loudness are also supported on this digital output
- an additional digital AES port which could be interesting to integrate the DAC into other recording environment

The unit that you intend to buy would only make sense it it would have
1. digital input(s)
2. also a superb D/A converter on board
But it does not have, so its only purpose is to add balanced phones to a unit which can't do.

Balanced connections are mostly used in a studio where you might have longer cables and where this special circuit ensures to eliminate electric noise and uses a higher signal level to allow for much longer cables.
To simply connect phones this is IMHO overkill and it does not make sound better, it simply avoids any potential additional noise (which most likely is not there anyway).
Some people might think it sounds better, because with balanced cables you might get a hotter / louder signal and to our ears louder audio sounds better.

So whatever comparison tests you might do later, you need to ensure equal volume levels.
Blind testing is also important.
This both to ensure not to become biased and misled by psychoacoustic effects.