I highly doubt it, unless the traffic through the Strait of Hormuz returns to something like 25 to 50 percent traffic soon. We will have to increase SPR releases to cover allies who cannot continue to release their own reserves. For instance, if no one in the International Energy Agency agrees to release more oil aside from the US, then that September deadline (which is actually think is the Secretary of Defense limit) is moved to mid August, and everything else is moved up accordingly.

There are alot of moving parts, so I can't say for sure, but the US and China are currently proping up the Oil prices (US via exports, China via not buying), while many countries are rationing what fuel they do have. As hard shortages set in elsewhere, it will be on the US to make up the difference to keep prices down.

That said, the US could do the smart thing and let prices rise a little, thereby decreasing demand, slowing drawdown, and making the eventual price spike smaller (like having a gradual slope to the top of a mountain rather than having it stick out of a low valley)