In someway yes.
But the outward garment is circumstance wise and should be cleared from greed though.

For example, MK Gandhi.. he was happy with his full clothes but prefered half naked not for show off or act of humility but because his subjects where themselves naked, no money for clothes.
Had it not been the case, he would have been well clothed. Likewise concerning his refusal to drink cow milk.. he chose not to drink because at that time Cows were not treated like one's mother.. knowing that being a politician he won't be able to do much, he chose as a matter of sacrifice not to have cows milk as a diet.

The outward dressing is dependent of the inward thought but the inward thought is independent of the outward dressing.
It is much of a mind game and purity, viz, renunciation of the fruit of action rather than action itself.