If the keys in your device match the keys in the network server (TTN Console), then: technically, maybe, yes; as soon as it transmits a packet using those secrets, the network knows how to handle it. However, it’s not like WiFi where a device is really “connected”. A device just transmits some data, and hopefully one or more gateways will receive that, and then forward to TTN, which hopefully knows how to handle it. Such gateways will also receive messages for other operators, and even messages that just use the LoRa radio modulation but without using the LoRaWAN network protocol, and will forward all of those. Typically, gateways don’t know what they’re receiving and forwarding.
So, by using ABP you really just skip OTAA by programming the “session” secrets into the device, rather than asking for those secrets* by using OTAA (which uses another secret, the application key).
*) and the non-standard network settings!