Simply put, no it does not.
This is a common misconception. I frequently see patients who come for a second opinion or because they're new to the area, and their parents tell me something like, "He patched for a few months, but it didn't help, the eye was still crossed in." Patching doesn't help straighten the eyes; it's done to help the non-patched eye develop better vision, but it almost never also results in better eye alignment.
Patching treats amblyopia, not strabismus (eye misalignment). Amblyopia occurs when a child's vision doesn't develop normally, and starts to "fall behind." It usually affects just one eye, but rarely may affect both. A child isn't born with the ability to see 20/20; this develops over time. If something is interfering with this process -- for example, eye misalignment -- then the brain often "picks" an eye and develops better vision with that eye, at the expense of the other eye. An analogy I often use is that amblyopia is like having one strong arm and one weak arm: naturally, you want to do everything with your stronger arm, and as you do that, the strong gets stronger and the weak gets weaker.
Patching the better-seeing eye allows the child to rely on their worse-seeing eye, and doing this helps them develop better vision with that eye, sort of like putting the "strong arm" in a sling and doing everything with your weaker arm. This process works best, and quickest, the younger a child is. By age 8-9 years old, a child's visual development is over, and patching is much less likely to be effective.
This can be confusing, because for a child with a misaligned eye that also doesn't see well, while they are wearing their patch on the other eye, the "bad eye" will be straight! This doesn't mean the eye misalignment is better, it just means the child is using that eye. Once the patch comes off, you'll see the eye misalignment again.
As patching continues, a child's vision in the non-patched eye should improve -- they should see better and better on the eye chart (note: preverbal children can certainly also develop amblyopia, and their vision is measured in different ways). However, if they have strabismus, the eye misalignment typically doesn't change much. That doesn't mean patching hasn't worked, as you now know!
For a child with both amblyopia and strabismus, the first step is treating the amblyopia, with some combination of glasses, patching, and/or eyedrops. Once the amblyopia has been treated successfully/maximally, the next step is treating the strabismus, with glasses and/or eye muscle surgery.
To learn more about amblyopia, check out this video from Dr. Weed.