Does std::deque support random access?

The cppreference documentation specifies "Random access - constant O(1)" (same as std::vector). There's a slight overhead from going through 2 pointers instead of 1 and keeping track of how many items are in the first bucket (so you know which bucket to check), but that's a constant and the big O don't care about constants.

Yes, you can see operator[] in the linked reference docs.