Closed SIP (or something) network

If I installed Asterisk on a laptop and had a router setup with wireless (but NOT connected to the internet), is it reasonable to say that I could use two smart phones with wifi to create a closed communication network using an SIP app on the phones? Looking for a cheap alternative to having to buy a bunch of walkie talkies for a short range need.

Absolutely. Asterisk does not require internet connectivity to function. You can create a completely isolated system.