I would imagine it would be the same as a normal Tamagotchi- Yes, you would be able to keep them. And if it is the same you'll also get to keep your Gotchi Points aswell.
6-15 / Adult (Note: the matchmaker begins visiting at around age 10)
16-99 / Senior
An EnTama is effectively paused while on its TamaTown (e-tamago) login password screen. Depending on how often you go on e-tamago this may delay its aging by a few minutes per day.
If you want to pause it for a long time, go to its clock set screen.