I like this change and am curious what type of overhead this has for the p2p network.

The overhead on the p2p network is very small: it's one small transaction generated by each of the producing witnesses. So in the normal case, it's 21 small additional transactions that travel over the network, but don't get recorded into the blockchain.

Do the p2p improvements you mention cover this additional overhead?

The p2p improvements vastly outweigh the additional overhead of these 21 transactions (it's not even close). Here's an example that only node operators are likely to understand of how substantial the improvements are with the new p2p code: on the mirrornet, with 2 nodes in the US and one overseas in Europe, the block offset times of all the witnesses are actually negative now (handling the same traffic as the mainnet).

There has been talks of speeding up transaction times to allow for better interactivity for users. Potentially 2 or even 1 second block times. The general feedback it is definitely possible at least in theory. Would 2 or even 3 second block time be possible with this additional overhead?

Yes, it won't have any impact at all. The latency improvements I mentioned above would probably allow 1 second block times, especially if we were willing to accept a few more missed blocks occasionally. But switching to 1 second block times now that the chain is launched still wouldn't be trivial, because there's a lot of code that assumes unchanging block times.

For most dapps they would see near similar speeds as HEAD but the protection of IRREVERSIBLE, which is a great best of both worlds scenario.

Yes, that's another of the driving reasons for the change.