For a private core node only, no disadvantages. As a private node (that only sync blocks from others and only add a tx to a block when you do it for yourself) the Tor connection is not making it slower or less available. If you lost a connection, you can wait a bit more for the next ones, not a big deal.

Things changes when you want to be a PUBLIC node that share more than leech, because you will have to be a reliable, fast and 24/7 online node SERVING the blocks sync fast.

Please make the difference between PUBLIC and PRIVATE nodes. Many people are confused, thinking that if they just run a bitcoincore node at home in full sync, automatically became a so called "Full Node". It is not like that, is a misconception.