I'd argue that a Stealth probe could be done. Not easy, but doable. I can think of several situations, including but not limited to turning a rogue comet into a probe and sending that through. The secret is not being totally invisible but looking like something that won't trip alarms. And yes, it would take awhile but if it is a strategic system, you could get some good basic info. Back it up with some spies traveling through to get updates a few weeks before the invasion. Humanti isn't perfect, you play on the weaknesses of the watchers and be devious...
Let us think about that "rogue comet" idea. First, you would need to identify the comet, and in a very short time, determine its potential path and then add your probe. Comets, while they do travel fast, normally take months to traverse part of a solar system as they do a swing around the star and then head back out. So, several months to years after you put your probe into the comet, you would get a snapshot of that part of the solar system that was near the comet path.
One thing that I've done in wargames, where possible in scifi RPGs that dealt with military themes, is the old trick of sending in a stealthed scout to jump way out beyond reasonable detection range and then send a probe on a ballistic flight through the system to get layout and passive sensor readings on active warships/defenses in system. Just do another jump or send another stealthed scout to a point opposite the first jump location to pick up the probe and download the collected data.
You are using a stealthed scout far beyond reasonable detection range, and putting a probe in a ballistic flight through the system.
First, if you put it into a non-powered ballistic path, then you will get a elliptical cometary orbit that does not cover the entire system. You would not be recovering at a point opposite the first jump location, but more than likely at a point within 90 to 120 degrees displacement from the initial point. That holds true unless you have the probe moving at a very high velocity, beyond the star's escape velocity. In our solar system, that would be, at the orbit of Mercury, about 151,000 miles per hour.
Next, using our solar system as an example, there are four gas giants that could be potential refueling sites, from Neptune at about 30 AU to Jupiter at 5.2 AU. Because of the need to give the probe a very high velocity, you drop it off at about 40 AU. You accelerate it to 10 million miles per hour, which as pointed out earlier will take about 5 days at 6G acceleration. So, either your scout has to be going that fast, or the probe has to be able to achieve that velocity on its own. At 10 million miles per hour, your probe covers an AU in roughly 9.3 hours. You want to check the outermost gas giant, Neptune, and the Earth, so your probe's path has to be close enough to those planets for its passive detection systems to work, and the planetary alignment must be such that the probe's path does not intersect with the Sun, or pass too close to it. So, you drop it off at 40 AU and pick it up at 30 AU, Neptune now being on the opposite side of the Sun. Total distance covered, 70 AU, multiply that by 9.3 hours, which is equal to 651 hours, or 27.125 days, or just under 4 weeks. Now, there are three other gas giants to cover, along with 3 additional planets, I am not counting Pluto because it is simply so far out, which you may not get any information on depending on where they are located in relation to your probe. That also does not include the Asteroid Belt.
Have you gained complete information on the system? I would submit that you have not, unless your probe's passive detection systems are so incredibly sensitive to detect ships at ranges of a billion miles or so. If your passive detection systems are that good, why are you bothering to use a probe? Simply send a few scouts in to jump a billion miles from the target planets, run your scans, and then jump back out.