This is something that I'm thinking, why won't the top 10~top 50 coins do it so that it can help their shareholders multiply their wealth. STEEM did it, and now XEM is doing a 1:1 drop for their XYM which has decentralization features to target the market cap too.
https://medium.com/nemofficial/public-testnet-and-symbol-launch-8470713a7962

Will the project feature push it, or will the mere fact that it came from NEM will most likely push their new token to success.

Will the price of an airdrop token increase significantly if it's under a big project/company? Or does it really depend on how that new token and its team perform?

I think both, if its a big project or token, then it most likely already has a solid team behind it. But yes, all these factors can really affect how the new token that will be on airdrop perform.

Having that 1:1 is also a good idea to attract new people to go for their new coin, most projects don't do that.

To answer your question, yes in a way. This may help people open their eyes and accept the technology even more.

XRP has huge technology and their updates are continuous. So its really hard to not believe in them.