Yes you can drive long distances on a plugged tire as long as the tire plug was installed properly so that it does not come out.
Although Tire plug manufactures recommend that you get the tire patched and only use the tire plug kit as a temporary fix the tire plugs can last the life of the tire if they are installed into the tire properly.
If you're taking the tire to a shop to repair the tire then having it patched would be the best option but if you need to plug your tire to get by with then it will work just fine.
A properly installed tire plug is a permanent fix and can last the rest of the life of the tire.
If you do not install the tire plug properly then it may only work as a temporary fix until you can get the tire patched or change the tires out.
I've installed tire plugs in my own tires before and they lasted in the tires until the tire wore out and needed replaced.
If you are able to follow the directions and install the tire plug properly in the tire you should be able to drive long distances and not have any issues with the tire plug coming out.
A tire patch is a much better option at repairing a punctured tire but tire plugs can work just as good if they are installed properly.