BitPay recently implemented BIP70. I noticed that BIP70 transactions leave metadata stored in my Electrum client (for instance, the vendor and invoice number associated with the transaction).
the only data that your Electrum wallet stores are usual things, using a BIP70 link is not going to change that.
the usual stuff are your addresses, keys, seed, transaction IDs, raw transaction hex, address descriptions, transaction descriptions,...
the only thing that may be different from when you create a transaction yourself is that it may store a description for the transaction which you can see in your History tab. if you don't like that, go there and clear it by double clicking on it.
Is any of this data transmitted to the blockchain?
you don't transmit anything to the blockchain, you transmit to the network and you can't transmit anything apart from your transaction to it.
I assume not because the payment details can all be specified beforehand off-chain, but I just want to make sure. And is the metadata in any way accessible by Electrum servers that I connect to?
there is not much "metadata" in this link as you think. you can see the details here:
https://github.com/bitcoin/bips/blob/master/bip-0070.mediawikisimply put, it is payment information which the merchant uses over an SSL secured connection so that it can not be manipulated by a man in the middle attack.
