Yes, if you set-up a local Blynk server within your WiFi network then it would work.
You wouldn’t be able to use Blynk push notifications, Email or Twitter, as these all use external resources, but everything else should work.
This example uses a Pi Zero as a hotspot/router so you don’t need any additional hardware…
Personally, I’d probably use a router as my DCHP server/WiFi Access Point/router and a Pi 3 or 4 as the server, but there are many options available, including running the server on a Windows 10 laptop.
Pete.