Can I use 3 wd livewire powerline adaptors with only one connection to my router?

I have not used that brand but as long as they follow the standard for homeplug-av, which almost all do, they will form in effect a switch. All 3 units will directly talk to each other. You will likely see some drop in throughput speed with 3 units since they form any-any mesh network which is not always optimal it you for example want 2 pc to talk to a router but don't actually need them to talk directly to each other.