No. To be honest, I like how it works better than how the island worked in the GC game. It was kinda annoying to have to hook up the GBA with link cable just to go to the island. Also, I didn't really go to the island that much in GC. Didn't feel like much of a point. Seems like more to do in NL's island. I'll probably go either daily or almost daily when I unlock it.
Do you have to unlock the island?
You just have to wait a few days.
Pay your 39,800-bell mortgage to trigger access to Resort Island.
[Tortimer] Kotobuki, sporting tropical wear, will appear "under the spotlight"
in the "dark room" as you load your game. That day, speak to him at the Wharf.
The following day, you can travel to Resort Island!
its a bit more than just a few days. heres it from Liquefy's guide: