Not unless everyone decided to sell all their assets at the same time. If the money supply is fixed, and the market size is constant, prices should fluctuate very little even as large amounts of fixed capital are accumulated and total wealth is increased.

Wouldn't technological development also need to be static in this scenario, as well?

It sounds like you're describing a completely static economy. The money supply doesn't change; the market doesn't expand or shrink; the utility value of goods doesn't improve. Has such an economy ever existed?

My point is that, even in such a theoretical and apparently stagnant economy, wealth is still accumulated and economics is very far from a zero-sum game.

By 'fixed money supply' do you mean literally no new coins/notes are 'minted' (except by exchanging smaller denominations for existing bills), or just that they are minted at a stable rate with no chance for government interference?