Normally, your node won't download any unconfirmed transactions until reaching the chain tip, as it can't verify the validity of those transactions. If you want to know the current mempool of a random node, then just trust a block explorer?
I'm not aware of any "importmempool" command in Bitcoin Core, perhaps you're looking at some other Bitcoin node implementation?
It has been requested, as you can see in this
Bitcoin Core PR review, but it does a different thing; it loads transactions into your node's mempool given a mempool.dat.