Technically, yes, but probably not how you’re envisioning.
If what you’re picturing is a craft dipping far enough into the atmosphere to look like it’s “in the clouds,” so to speak, and then exiting again back into space, then probably not.
However, you may be able to achieve something that at least somewhat resembles what you're imagining. Here's some factors worth considering:
It sounds like you need your craft to be in orbit for a while before it performs this maneuver. If instead you want your object to originate from someplace outside the immediate system (e.g., launched from another planet) and directly descend into the atmosphere once it arrives, then essentially what you're describing is an extremely dramatic version of aerocapture.
Either way, the key here is drag. Notice that with an aerocapture maneuver, the portion of the atmosphere targeted for increased drag is still extremely thin. This is because, at orbital velocities, just a tiny amount of gas molecules is enough to cause a whole lot of heat and friction. So, to a casual observer, craft undergoing an aerocapture maneuver do not appear to be noticeably “inside” any perceptible gaseous medium.
If you absolutely need to construct a craft that is able penetrate deep into the atmosphere of a gas giant at orbital velocities and then exit, then it would need to be:
- traveling an order of magnitude faster than satellites typically travel, in order for atmospheric drag not to slow it down below escape velocity;
- composed of magic space-metal to withstand the extreme heat.
If your craft is originating from outside the immediate system, then as long as it’s traveling fast enough to maintain atmospheric escape velocity, but slow enough not to exceed orbital escape velocity (and it doesn’t vaporize from the heat), then, yes, you could theoretically perform an insertion maneuver this way.
Alternatively, if your craft must perform this dive from an already-stable orbital position around the planet, it would need a crazy amount of thrust to begin the maneuver. (E.g., you include some propulsive means on the craft strong enough to boost the object back up to an appropriate speed or altitude. But again, the thrust needed would be enormous.) Otherwise, you'd just be initiating a skip reentry.
In both cases, it all depends on the aerodynamics of the craft, the atmosphere of the planet, the altitude and speed of the craft, and so on. There are many variables.