That depends on exactly why Nicaea fails to conquer Constantinople.
If Nicaea starts out with weaker and less capable leaders and a lot more bad luck than in OTL, then it is possible that Nicaea fails to conquer Constantinople, and then there's even the possebility that the Latins or the Rum sultanate conquer Nicaea.
However, if Nicaea remains as strong as it was in OTL, then the only the conquest of Constantinople by another Orthodox state (such as Bulgaria or maybe Epirus) could really prevent Nicaea from conquering Constantinople.
If another Orthodox state succeeds in conquering Constantinople and keeping the Nicaeans out, then Nicaea would still remain one of the most powerful states in the region.
And if whoever conquered Byzantium (propably the Bulgarians) is so powerful that the Nicaeans won't even bother trying to take Constantinople from them, then Nicaea will become more involved in Anatolian politics.
After the Mongol conquest of the Rum Sultanate and its gradual collapse, I can see the Nicaeans take advantage of the situation as they try to keep Anatolia and the many newly formed Turkish principalities under their control.
The OTL Byzantines didn't take advantage of the collapse of the Rum Sultanate, but that had more to do with mismanagement, lack of capable leadership, fear of the Mongols, political developments in the Balkans, and a sheer lack of interest in Asia Minor on the part of the Byzantines.
But as long as TTL's Nicaea doesn't have any conflicts with TTL's Byzantine empire and as long as its leaders that are at least moderately capable, TTL Nicaea won't have any of the problems that prevented OTL Byzantium from interfering in Anatolia.