So what vehicles were used as Interceptors for the UEDF in the 2RW

[Rabid Southern Cross Fan]

Okay, now that we're getting somewhere about the Logan, another rather obvious problem to tackle is just how the UEDF had its mecha and vehicles organization and their roles. We know the Logan isn't used as an Interceptor because it doesn't need to be one. Its job is to pound enemy mecha with its guns, aerospace/base defense (maybe even close-in space fleet defense), and presumably boarding actions in space. Well, what about interception of enemy fighters like the Gnerl? Well, that falls to 3 vehicles: the Pegasus-class Assault Shuttle (which also acts as a Corvette in fleet formations, providing anti-fighter screening fire), VF-5 Sylphide Veritech and the F-110 Falcon II.

Now the Sylphide and Falcon II are well established as such, given we see them time and again used in that role (with the Sylphide actually being the Mutli-Role Veritech Fighter, while the Falcon is obviously mainly an Interceptor). The RPG gets the loadout on the Falcon wrong as it almost assuredly uses beam cannons instead of an older rotary cannon and it can carry on each of its outboard nacelles 2 large missiles (drawn to basically be the same as the Python on the Logan and Sylphide, but WAY longer since the Falcon II is 19m long). The internal missile bay is a guess, but an educated one all things considered.

But the Pegasus probably seems like the odd duck in this. But we have direct evidence for this from Episode #46 Star Dust:

CONTROLLER: Enemy ship at 30,000, bearing zero, mark 29.

SUPREME COMMANDER LEONARD: Good, our friends have taken the bait.

EMERSON: Hmm. Scramble all the interceptors!

CONTROLLER: Attack wing seven, you are cleared for launch. Interceptors are away and steady. Apogee in two minutes.

The Interceptors are the Pegasus shuttles and Attack Wing 7 includes the Logan's carried in their hangars. Given we see the beam cannons on the Pegasus are quite capable of killing both mecha and larger craft, it would be perfect for the job of closing with an enemy and obliterating swarms of mecha. Also, given that it can rapidly insert into orbit as well as make the crossing from the Earth to the Moon, it could stay on station a long time as well as the fact its blisteringly fast (Earth to Moon transit is ~5hrs).

The Pegasus (like the Roc) actually seems to make up the vast bulk of the Earth's at home portion of The Interstellar Fleet. They likely suffered grievous losses to The Masters ships, given they were pitted against the God-tier foes of the Robotech universe.

[ShadowLogan]

We know the Logan isn't used as an Interceptor because it doesn't need to be one.

I have to disagree here.
1st "Star Dust" Dialogue DOES connect it to that very role by Sean and a PA announcer via audio (what is the interceptors could be the Logan, could be the shuttle as you suggest, or it could be both of them in a "team" setup)
2nd "Southern Cross" had Marie's squadron to lead the attack, but was changed at the last minute. Unless Marie was really to operate some other platform for that action than what she would eventually use for this episode and her next x3 combat appearances it would be a Logan.
3rd "Volunteers" could be argued had the Logan operating as an Interceptor for the shuttle (cause lets face it the VHTs they carried onboard can't do the job)
4th "The Trap" could also be argued had the Logan operating as an Interceptor when it defended the 15th from that airborne bioroid

While one could make the case the Logan doesn't have to be a primary interceptor, it does seem like a role it was expected to operated in. The only episode with a Logan that does not suggest this is "The Invid Connection" where it is only really shown in a static shot in the background hovering about (loitering but ready to dash off for an intercept?).

[Peacebringer]

The UF-14, in my mind, is always Anti-UN and a great interceptor.