Kind of.

There is no "the pool" or "the mempool" (which is what I assume you are talking about when you say "the pool"). Rather each node maintains its own mempool which may be different from another node's mempool. Because each node receives a given transaction at different times, the amount of time a transaction spends in the mempool will also vary from node to node.

However, you can still run a node and track how long a transaction spends in its mempool before being included in a block. In fact, Bitcoin Core already does this in order to do fee estimation, although the raw data is not exposed to users.