Is there a way to determine if a collection is a palindrome within a time bound?
If n is the number of words, it's impossible. It would mean that any roblem with just two words could be solved in constant time. But you could have two words of arbitrary equal length, and the time to confirm that one is the other reversed is unlimited if the length of the words is unlimited. 

PS. Your edit changed this from a rather interesting problem to one that is really boring and trivial. You take an array with 26 counters, one for each letter, initialised to all zeroes. You go through the letters, and for each letter you increase the corresponding counter. When you are done, you check that there is at most one odd counter. 

When you ask a question, it's only polite to take your time to state the question properly. Your original question has nothing whatsoever to do with the edited one. 

And if you haven't figured it out: In a palindrome, the first and last letter, the second and second to last letter, and so on, are equal. Which means you have even numbers of each letter. There may be one letter in the middle (like in oxo) that doesn't have a match, or there may be none (like in otto). Which means at most one letter has an odd count. So to figure if a palindrome can be formed, just count the letters.