Does it affect the speed or efficiency of Google Search if I just put the words in randomly as opposed to some specific order?
Word order does affect your search results. For example, try the following two searches and observe the differences:
Not only the number of results but also the order of mutual results are different. Note that if you put your search terms in quotation marks, Google looks for the exact sequential words. For example:
This kind of search will, of course, lead to less number of results.