Kind of but no, because the Fog Ship also makes you ageless.
Fog Ship Guide: Come with me upon this ship, where time governs us not.
Fog Ship Guide: Come... Be eternal...
Razro: If I stay here, my life will never end?
True Runes let their bearers age to maturity.
Originally the story was that Ted lost the Soul Eater for a while and that's why he aged when people pointed out that he did in fact age after Suikoden I released. This plot hole was later closed when Konami retconned how True Runes work to let their bearers age to a certain point if they get them very young.
However, Ted's official backstory never changed so it remained canon that he lost the Soul Eater for a time despite the need for this plot thread being gone.
The Fog Ship actually exists to explain how Ted lost his Soul Eater without aging.
Doctorum Non Urina Singulus.