We have an assumption that the constant function doesn't deal with arrays - the number of elements involved is constant.
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In theory yes: If the state database gets bigger while the amount of fast-accessible storage on the validating nodes doesn't, it'll be more likely that your data access will require reads that take longer, ie something that would have been cached in RAM will have to be read from disk. This will mean it takes longer for a node to validate a block. But it shouldn't alter the time it takes a transaction to confirm, as that depends on the block interval, which shouldn't change unless something goes very badly wrong.
You generally shouldn't have to worry about this, but you should worry that the gas price may go up and/or the block gas limit may go down.