Almost all of the old school Aikido instructors I've met have all been experienced Judoka. Ask them how that has helped their aikido.
Judo teaches you how to fall from a variety of quick throws (you can't roll out of them like in aikido). Learning to take gook Judo ukemi is very important, and will prevent most injuries.
There are 8 ways to unbalance an opponent in judo. Having a deep understanding of this can only benefit you.
Judo teaches you how to think on different lines of off-balance. (down the line of the feet, and perpendicular to that line).In that way you can set up uke into whatever position you like.
All circular motions in Aikido are really just linear breaks one after another (down the line, then perpendicular, then down the line, then perpendicular etc), So by studying Judo, you can get a deeper understanding of these off balances.
Judo is a grabbing (close contact) art, while Aikido is mostly at arms distance.
If you ever get to close to an attacker, Judo will definitely help you out, not to mention the ground work that you learn.
In Judo (like aikido) strength will come from those who lack technique.
As far as an ("Aiki" mindset needed for Aikido techniques), I'm not sure what this is, but I'm sure Judo won't hinder it.
hope this helps!