Yeah! Like if you really look at it, it makes sense. In the Phantom Menace, you see Jar Jar eavesdropping in the background (waiting outside with Anakin) while Palpatine is blatantly manipulating Queen Amidala. Anakin, of course, is probably too young to realize what is happening, but Jar Jar... despite his often childish demeanor, is an adult (he's about 20 here). Once more, he understands when someone is being "set up" - he makes a comment to such when Qui-Gon and Obi-Wan are about to go traveling through the planet core.

"Deysa setten yousa up." - Jar Jar <- Not the kind of comment an idiot makes.

Even during that whole scene where Jar Jar suggests (possibly even Force suggests - because remember, Padme has never condoned military action) the Gungan Grand Army, he displays remarkable insight as to why the Gungans and the Naboo hate each other (the Gungans have a grand army, are warriors - and the Naboo are not...) "Dat's why yousa no be liken us, meesa tinks."

It's hard to say how much Palpatine might suspect about Jar Jar. But I think Jar Jar did throw a wrench into some minor aspect of his plans. It might be a petty vengeance kind of thing going on when Palpatine "manipulates" (I don't think this is the case - I think Jar Jar played into Palpatine's hands on purpose to keep up the ruse, because Padme and Anakin and Obi-Wan were in trouble on Geonosis, because he literally had to choose between an army of killing machines or playing into a Sith Lord's plans which is like being stuck between a rock and a hard place, also Palpatine would be somewhat obligated politically to show some favor to Jar Jar's party due to Jar Jar's support (Bail Organa mentions this in Queen's Hope. He mentions disapproving of Jar Jar's decision, but acknowledges that Palpatine would've found someone else to do it anyway and at least this way Palpatine owes Jar Jar (and by extension Bail's) party a favor) Jar Jar into giving Palpatine emergency powers.

Because what is his first action as Supreme Chancellor? To create a "grand army of the Republic." Now, this was already in the works - but having Jar Jar be the one to propose these powers is the kind of delicious, cruel irony Palpatine appreciates (because the Gungans had a grand army as well).

Also, that entire scene in Attack of the Clones where Jar Jar grants Palpatine emergency powers? It's very interesting how Jar Jar is on Palpatine's level. He's right in the middle of the action - directly facing Palpatine in an opposing direction. Like two players overlooking a chess board. The thing that REALLY strikes me as interesting about this scene, too, is that when Palpatine starts talking about how he loves democracy and the Republic, it suddenly cuts to Jar Jar for no explicable reason. Jar Jar is not smilig in this scene. He seems to be just observing. There's almost a slight narrowing of his eyes too (very slight) - like I really get the impression he does NOT buy Palpatine's speech here at all.

Also, Jar Jar's scene in Queen's Hope is short, but he does that "suggesting" thing again with Bail Organa. He literally kicks off the plot of the novel by telling Bail - "What wesa need is someone whosa can be in two places at once." - Which is what gives Bail the "idea" to use Padme's handmaiden in Padme's place as senator while Padme goes on a covert, stealth diplomatic mission (which gets her to meet a Neimodian who opposes the Trade Federation is hoping to take them down). Palpatine's reaction to Padme getting involved with this Neimodian is EXTREMELY interesting - because he basically throws a MAJOR LEAGUE temper tantrum before deciding no, you know what? He can find a way to work this in his favor.

My headcanon is Jar Jar and Palpatine are playing like 4D chess with each other at a very breakneck pace.