Bitcoin Core would send transactions only when it detects an internet connection and is connected to its peers.
Lets say you gave me your bitcoin address to send you 0.1 btc,
could I do the following offline
1- open bitcoin core
2- input your address and value of the bitcoin I want to send, in this example, it's 0.1 btc
3- click send and input the wallet password if there is one
and when bitcoin core is online,
- the transaction gets broadcasted to the network/blockchain and eventually you will get the 0.1 btc I have sent you