This will certainly give you better connection experience. However, allow plenty of time: each extra independent ticket adds additional risk of misconnection.

I flew Vistara AMD-DEL a few weeks ago and found the experience to be pleasant, like what 9W used to be when it was new.

However, good as Vistara is, flights can be delayed for reasons beyond an airline's control. Also, while AI would have checked your luggage through to DME, with Vistara you'll probably have to pick it up in DEL and check it again with AI. All in all, allow plenty of connection time in DEL.