I'm not familiar with 10- and 11-speed chains, but if the spacing between the plates of the two types of chain are the same then you could try your idea. But that would mean the 11-speed chain has thinner plates, which doesn't make sense to me. If the 11-speed is narrower because the spacing is less, then it won't fit on the teeth of your cogs and chainring.

Short chainstays are a feature of folding bikes, and as xenologer pointed out ^^ this can be a complication with wider cassettes. You may have to rely on optimal derailleur adjustment and lubrication to minimize the noise.

I have two Dahons and a Tern, but they all have internally-geared hubs, which side-steps this problem entirely!
Steve