Fluff-wise, the Collegia Titanica is a part of the Adeptus Mechanicus.
They follow the orders of the Terran council and might fight alongside Adeptus Astartes from time to time and even accompany them on lengthy campaigns as well if the need arises but they would most probably not adorn their sacred vehicle with Astartes Iconography other than the occasional symbol to honour a particular hero or campaign from/with the faction they have been assigned to.
But if a Collegia Titanica-sector has been assigned to join forces with another part of the Imperial force they will bring their own fleet since the maintenance of the titans is a task that only very specially trained personnel can do.
The seasoned crew of a Titan will very often suffer from severe hubris and would not suffer their battle god the symbols of some other faction than their very own.
There have been occasions where a titan and it's crew have been enlisted by an Inquisitor and have been forced to change their heraldry to that of the Inquisition but that is a very rare sight.
So, fluff-wise, no, it would not be appropriate to make an 'Ultramarine Titan'.
But there is always the opportunity to give the titan your own story. Perhaps the titan crew died in a campaign and some Marine hero with latent psycher tendencies managed to connect to the titan and do something awesomely awesome and save the campaign and so on and so on and 3. Profit, Ultramarine titan.

This is a fantasy world after all and the only limit is your imagination.
