Live Chess (timed) Vs. online chess

so I was wondering, with the fact that live chess games are 30 minutes or shorter and "online chess" can have 24 hours or longer between turns, does learning how to play live chess and playing "under pressure" make you a better player at online chess concidering the pace is much slower and you have more time to concider your options?

Probably. Playing chess in general will improve your chess. There are benefits of playing both live chess and online chess. Playing live chess has extra benefits of improving your time management skills, quick tactical calculations, and so forth. Whereas online chess would allow you to think a lot more deeply about various different things. Positional play, development of a plan would be a lot easier to come up with in an 24hour game rather than a 30min game and so on. 

So live chess would help me in spotting patterns and position quicker and the online would help me for tactics and strategies to play once I have spotted those patterns?

Live chess is probably better than online for improving just about every aspect of chess. The main difference between the two is that you can spend a very long time calulating long forcing lines when playing online (with the help of the analysis feature too) wheras live you must use your intuition.

Calculating long lines does nothing to improve your understanding of chess tactics or strategy. Using your intuition does, be it learning from your mistakes or otherwise.

I don't think that playing quick live chess will help a whole lot in online chess. I love online chess. The best part about it is I usually think for three or four minutes about every position. In live chess where you are playing 15 or 20 min/game you really only get to think like that for a move or two per game. The rest of the time maybe you spend 20 to 30 seconds thinking each move and then in the last two minutes, you just end up making moves without really thinking, just reaction.

I feel like I get a lot more out of being able to think for a few minutes about each position than rushing around making moves without thinking.

Whatever skills you learn about playing in time pressure in live chess aren't really applicable to online chess since you are never under time pressure.

Essentially playing chess regardless of time will improve your chess skills. I agree and disagree with StartlingNewEvidence, calculating long lines will improve your calculation skills which is a large part of chess. Obviously using the analysis feature on online chess to explore lines wont do much for your calculation. My advise would be to try to calculate it out in your head and then check it with the analysis after.