In regards to the OP, if the I Corps made it to the right rear of Howard's XI Corps then Hooker's flanks are completely secured. The I Corps was to be stretched from the right rear of XI Corps to Ely's Ford at the Rapidan River. Jackson's assault succeeded OTL more due to the fact that they outnumbered XI Corps 2-1 than his tactical skill. With no flank to strike, the odds greatly evened and Jackson's faulty tactical deployment, it is very likely that Jackson's attack splutters out against the combined mass of I and XI Corps. However, even with the failure of Jackson's attack, Jackson's Corps still represents a powerful threat on Hooker's flank. Whether Hooker decides to go forward and counterattack is up in the air.
Even without Hooker directly counterattacking, Lee would be unable to maintain his line when one considers that Sedgwick's VI Corps successfully storms Marye's Heights on May 3rd, putting Lee's rear in peril. The Army of Northern Virginia would be obliged to give up their position and fall back to Spotsylvania Court House or further south to North Anna. Given Sedgwick's rather timid and sluggish performance during that campaign, there is a good chance that Lee can get away if Hooker doesn't go on the offensive.