On paper yes, but doing so also reduces the time for the burn. Probes have very low-thrust engines. Even during a jupiter slingshot they barely have time to accellerate much on thier own. Often they do not bother, relying totally upon the grav assist to accellerate. The danger too of a closer approach is that something gets miscalculated. Get too close and an inevitable tiny misalignment will throw you onto a wild unwanted trajectory. There is no gps out there. Knowing exactly where and how a probe is moving isnt easy.