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Only if you ignore his performance prior to that. Grant had commanded armies since the beginning of 1862, had outmaneuvered his opponents and captured two whole armies in the field at Fort Donalson and at Vicksburg, cut the Confederacy in half, and beaten every general Davis sent against him.

Having groups of Naval vessels which he could use to ferry his troops across the river made that possible. Once again, his great victory is more of a function of having superior assets to call on, and not so much due to his own abilities.

What would he have been able to do to take Vicksburg without those ships?

The simple fact is Grant conceived the plan, coordinated with the navy, carried out the plan and captured Vicksburg.
That’s what capable generals do. They plan, used the assets available and execute the plan.

Having groups of Naval vessels which he could use to ferry his troops across the river made that possible. Once again, his great victory is more of a function of having superior assets to call on, and not so much due to his own abilities.

So you give Grant no credit for the underlying strategy of running the Vicksburg gauntlet with his war ships and then transporting his army across the Mississippi, cutting itself off from its supply lines, and then outfighting and out-maneuvering both Johnston and Pemberton in a series of battles resulting in Pemberton's army trapped in Vicksburg and Johnston's army impotent in Mississippi? Congratulations! That puts you in opposition with just about every historian to every study the Vicksburg campaign. Not at all surprising.

What would he have been able to do to take Vicksburg without those ships?

Grant took advantage of the tools available, just like every great military commander does.