The odds of being picked remain the same. The only issue is when there are people who win and only need one seat, or if there are an odd number of seats to begin with, where at a certain point,it will get down to one seat, at which point, the system will keep picking single entrants and discarding people who need two seats. So, by that logic, sure, a person who wants a single ticket will always claim their ticket, but if there is one ticket, and you win wanting two tickets, you will never know you were that close.
Of course, if you need two tickets, then your +1 should also be entering the lottery, which would seemingly stack the deck in your favor over the single entrant.