Yes, it's possible. I was going to suggest Target Disk Mode, but depending on the age of the old and new MacBook Pro's that might not be possible. The older ones have it for sure, the newer ones, not. If you're going to use Migration assistant, you could use either USB, Firewire or Thunderbolt. between old and new MacBook Pro, you just have to make sure that the old MacBook Pro boots and powers up OK. If you had a Time Machine backup of your old Mac, you could use that with Migration assistant. However, I don't know if you do or not, I was hoping you did, but I can't be sure on that......
and yes, you can use local wifi---just make sure that the MacBook Pro's were/are on the same physical network. Though how you're going to check that on the old MacBook Pro with a broken screen is trickier. Maybe you can borrow a monitor and plug it in.
anyways, TDM works on the following MacBook Pro's......
here's Apple's webpage on it, if that helps you out any: (yup, link)
https://support.apple.com/en-us/HT201462
anyways, that's all I have for today
john b