Yes, it's implied that he does.
In The Fourth Apprentice, Tigerheart is by Dovepaw's side at various times during their journey to the beaver dam to unblock the water. When they return to ShadowClan camp after completing their quest, Tigerheart 'bounded up to Dovepaw and rubbed his muzzle against hers.' He said that he would miss her, and asked if he would see her at the Gatherings. In Fading Echoes, although he doesn't tell Dovepaw why he was on ThunderClan territory, he asks her to keep his secret. At one point, he comments: "On the journey upstream, we were almost...friends. If we were in the same Clan it would be so easy...."
Because Tigerheart doesn't have the same cold heart that Tigerstar and Hawkfrost do, I suspect his feelings for Dovepaw will eventually cause him to help her somehow when the battle between StarClan and the Dark Forest forces all cats to choose a side.