No, lasts until dispelled is not a duration
The duration of a spell is explicitly given in the spell text:
Duration: Concentration, Up to 1 hour
The effects of a spell can last longer, as stated in the rules - in this case potentially until dispelled, but the spell itself is no longer active, only the effects of it. For example, the hit points cured by cure wounds persist until destroyed, but that doesn’t mean that the cure wounds spell’s “instantaneous” duration is extended until that happens. The effects linger, but the spell that created the effect has ended.
Spells only do what they say they do. In this case, the spell says its duration is up to an hour, and its effects can last until dispelled. The spell text does not say its duration is extended indefinitely if you concentrate for an hour, so it is not.
For the purposes of combining spell effects
The second casting of True Polymorph will suppress the first casting. If that spell is dropped before an hour passes, the target will revert to the form it took from the first True Polymorph. If the second casting is concentrated on for a full hour, the from it took from the second casting will persist as well, suppressing the effect of the first until it is dispelled.