That's fine.
Just note that if your using a PAYG SIM you need to make sure it doesn't expire by sending messages regularly.
Also you'll have to keep an eye on the signal to make sure the network is still working. Pretty much all mobile providers have set dates to decommission older phone masts, some have started already.
You can't rely on your mobile phone signal as a tell, it will likely use 4G assuming your phone is newer than your alarm...
Monitoring has the benefit of polling which continuously checks the device can send/receive messages for those times you need it.