I think that the mempool size is too large and it would be difficult to share their mempool state, but maybe I'm wrong...
Although each node have different maximum mempool size, usually it has 300MB capacity. But since it's used to store deserialized trannsaction, raw transaction size on it's mempool probably has half or less size (150MB or less). With today's hardware and internet connection, sharing 150MB or less transaction isn't difficult task.