Can I run sequences, without my controller being plugged into internet.

Thank you so much to everyone for your help so far. I have managed to download sequences and have them paying through my singing trees.
I am almost ready to start setting up my display, I am wondering can I play my sequences without the controller being plugged into the internet?

Yes, you can play sequences without having internet access. But you'll still need Ethernet cabling or Wi-Fi to allow your controllers to receive data from your show player (which could be an Raspberry Pi with FPP or Windows/Linux PC with xSchedule). One caveat is if you use rPi to run your show and this will not have internet then look into the real time clock module to ensure it keeps accurate time for scheduling sequence playback.

With my show I have a separate wired network for my controllers and PC running xSchedule. This PC is the only device on this separate lights network that also has internet access via my home LAN. This is possible because this PC has two separate Ethernet ports, but you could also achieve this with one Ethernet port and Wi-Fi.

In addition to what Ryan says, some (but far from all) of the controllers can play in standalone mode without any added player or Pi and need no network at all once they are loaded up with sequences. Again, some of them won't remember what time it is if you turn them off and back on... if you configure it to auto-start the show though, they'll just start playing when the power kicks on so you can put the power to them on a timer. (My brother does this with a little BBB player serving his apartment window - with a Rosa wreath, 6x50 matrix, 6 snowflakes, and some C9s, maybe 1000 pixels total. Pretty sure his system is to run the cable from one room down the hall to the other, load it up, then put the cable away to keep it from being a tripping hazard.)