Definitely, but thankfully, it is a positive sum game.
First thing, you won't keep your bargaining chip for long. If a country manages to find a vaccine, others will follow soon enough. Besides independent research and reverse engineering efforts, it is foolish to think that the US doesn't have spies and hackers targeting China.
So in order to use that "bargaining chip", the vaccine has to be at least as valuable as what you are asking for in exchange. So while it may cost a lot to the country that doesn't have the vaccine, if it took the deal, it means that the cost is less than not having a vaccine at all.
In the end it will be used to help as many people as possible, because it is the only thing a vaccine can do. Unless someone wants a full-on war that is. But if major powers really wanted the worst, there is a pile of nukes that is ready to make the whole pandemic look like a joke.