No, a node is not going to present a transaction that it has not beforehand provided to the requesting peer—that will make nodes trivially fingerprintable. Additionally, it will be costly for nodes to lookup arbitrary transactions, as RedGrittyBrick identified within the different reply.

Bitcoin Core makes no transaction propagation ensures, we solely have ensures for block propagation.

Bitcoin Core will solely relay every transaction when it first learns about it. It is going to at that time announce its new stock to all its friends, which can request the newly provided transaction after the announcement.
When a brand new block is discovered, saying the block to a peer additionally declares all included transactions, probably a second time.