As long as you draw the whole deck before shuffling discards, it doesn't matter. Simply put, all cards in a well shuffled deck are equal. (Or have an equal probability of being this or that.)
Splitting the deck, drawing in the wrong order, or intentionally drawing from the middle of the deck, or even shuffling the deck between draws does not matter, if there's no way to gain knowledge of the cards, either from how the deck is used in the game, or by (accidental) peeking.
However, in games where (e.g.) used or discarded cards are put back to the bottom of the deck without a reshuffle, it obviously matters. (The mechanic is usually something like draw two, keep one, put the other to the bottom of the deck.)
Shuffling the discards in to the deck before all cards are drawn once, will also change the odds slightly. Also, in some games, players may actually want to draw cards from the original deck (before drawing cards that have been discarded and reshuffled once), so when the end of the deck is near, even minor rules about the order of almost simultaneous draws will matter.
Incidentally, since Ticket to Ride was mentioned: well shuffled is also a key word, since a badly shuffled deck might very well have bunched remains of previous sets.
Of course, any of that doesn't stop people from being superstitious. :) I'll admit to sometimes drawing from the middle of a shuffled deck in cases where my previous draws (from the top) have been utter garbage. I know it doesn't change the odds (and if it did, it would be cheating), but only makes me feel better by being able to act out on my misfortune. ;)