Is the SegWit address an "bech32" SegWit address (ie. a "bc1" address) from Electrum? Or is it a P2SH-P2WKH address (i.e a "3" address)?

If it is bech32, then I don't think you can do this... If it is a "3" type SegWit, then I would think that it was possible... Unfortunately, I don't have any BTG in a SegWit address to test with... but theoretically, it should be possible to move the BTG by manually creating a transaction in BitcoinGold Core.

I helped a guy this morning move his BTG from an Electrum 2FA wallet by manually creating and signing transactions, so I would assume that you simply do the same thing in BTG Core but with a SegWit address/private key