Endless Waltz was first a three-episode OVA that came after the television series and the Gundam Wing Operation Meteor I & II: Odds & Evens OVA. While with a different director than from New Mobile Report Gundam Wing, the OVA was scripted by Katsuyuki Sumisawa who did script the television series.
Quatre first appears with Duo, ready to send their Gundams along with Trowa and Heero's along with a disposal block to the sun to be destroyed. Duo notes that Wu Fei didn't send his. Quatre replies that Heero and Trowa sent theirs right away. It is basically just chatter. Duo wonders what everyone is doing.
So, pretty much neither of them have really kept in touch with each other or their fellow pilots it seems minus Duo and Quatre. Basically, nothing is given in this scene in regards to how Quatre feels about Trowa.
The next scene that has any dealing with Trowa and Quatre is after Trowa, Heero and Duo have stabilized Colony X-18999. Despite saving colony, Dekim has escaped with the Serpent Mobile Suits and heads to Earth. Trowa says it is over when members of Mariemaia's army are outside the control room, but soon Duo tells him it isn't and shows on a screen mail sent by Quatre. He managed to save the Gundams back from their trip to the sun. Trowa, Heero and Duo listen attentively. Other than the comradeship and ability to work as a great team, nothing is hinted at here when it comes to Trowa and Quatre.
When Trowa and Quatre meet up again, it is to go to war. With Duo they head out in their Gundams to fight. There is no real interaction between them other than observing and strategizing.
The last scene they are seen together is again with Duo. They are on top of a hill, looking down at their Gundams. Their Mobile Suits are destroyed then by the self-destruct mechanism. No longer needing to fight, Trowa notes that he is nameless again. Quatre turns to him and tells him,
"I don't think it makes a difference. Trowa is Trowa."
Duo agrees with this and comments that they have a place to go back to. Trowa smiles a bit and agrees with this.
Again, nothing really comes of this. Sure, Quatre is the first to respond and encourages Trowa to keep the name they identify him with, but unless you read into it too much, nothing is really there other than reassurance of a friend.
At the end of the OVA there are scenes of what lives the former Gundam Pilots are doing. It shows Trowa returning to the circus and Catherine waiting. She smiles and when he arrives at the entrance she turns and they both head in together. Quatre's scene shows him and the Maganacs returning from space and being happily reunited with the rest of their team.
In the movie the footage for the ending is different, but still makes no difference in hints. Quatre is working on reconstruction with the Maganacs. Trowa is back at the circus and is performing with Catherine. Basically they are nowhere close to each other and based on the beginning of the film, they likely aren't in contact.
From what is seen, nothing romantic is hinted at all in Gundam Wing: Endless Waltz when it comes to Trowa and Quatre. At the least there is trust and fondness as soldiers in arms between them. At most there is a good friendship.