It's possible.

Bell felt that human operators gave better service, but after the operators strike of 1920 investments were made in switching hardware to support direct dial. The first dial tone service in Atlanta began in 1923, but adoption was gradual. Nationwide, 65% of telephones were using dial service by 1947. By 1956 the rate was 89%.

The procedure for using a switchboard was that when the caller took the phone off-hook it would cause a light to come on at the switchboard. The operator would plug one end of the patchcord into the socket corresponding to the caller and ask who they were calling. If it was a local call then the operator could complete the call by plugging the other end of the patch cord to the destination. When the call was over the lights would turn off and the operator would unplug.

Long distance calls required to operator to connect to other operators via the trunk lines, and patch it through.

In some old movies there is the trope where the caller bounces the hook up and down to make an urgent call. This just made the light flash on the switchboard. I don't know if it was effective.

If the callee hung up very soon after picking up, it's possible that the operator might ring back to check that the line was working. Otherwise it would just be silence.

If you had dial service (like in the 70s) it depended on who was calling. The line didn't drop until the caller hung up. If the callee picked up the telephone again and tried to dial someone else they would still be talking to the first caller. If, on the other hand, the caller hung up, the callee would get a dial tone.