Not really. Making mempool policy stricter may eventually cause blocks to exclude transactions infringing on the new rules as hashrate updates. However, as long as just a small portion of the nodes (perhaps as little as 2–5%) run with the old rules and at least one miner has not upgraded, the transactions would still appear in blocks.

On the other hand, a softfork enforced by a majority of the hashrate would actually reorganize offending blocks out of the best chain since it would actually be a consensus rule rather than a policy rule.