Regular patronuses do not hide a person from dementors, so if a person came in with the true invisibility cloak, but not a true patronus, they would be noticed by the dementors as soon as they gave it to the escapee.
On further consideration, I suppose that it might work if you could slip them into a bag of holding and conceal them on your person, but the implications of readily available bags of holding that can contain untransformed people without harming them are so broad and incredibly broken that I'm inclined to suspect that you simply can't do that, first because it would be a story breaker, and second because people would do it on a regular basis and it would have come up before.
The fact that nobody is supposed to be holding the idiot ball doesn't mean that everyone is particularly intelligent or rational (in the wizarding world, this is clearly more the exception than the rule) or that they have access to the same information we do.
Remember that the Deathly Hallows, in canon, were widely believed to be mythical. It's hardly fair to expect these people to even keep in mind that they exist, let alone contemplate exactly how powerful they might be and account for them in their plans.
Keep in mind that when we, the readers, are encouraged to think of artifacts of great power in this setting, the Deathly Hallows immediately come to mind, but to a person who's grown up in the wizarding world, they're just three out of perhaps thousands of possibly-real objects out of myth and story. From their perspective, it could be equally plausible that someone dominated the will of the dementors using the hand of Vecna or something.
Regular patronuses do not hide a person from dementors, so if a person came in with the true invisibility cloak, but not a true patronus, they would be noticed by the dementors as soon as they gave it to the escapee.
They would be in the same situation as a regular intruder, which are not all that rare, and whom the Dementors usually don't seem to immediately report about (otherwise the aurors would have wondered why that hadn't happened and have been much more alarmed).
...Remember that the Deathly Hallows, in canon, were widely believed to be mythical.
- This thread has run its course. You will find newer threads in the discussion section.
Another discussion thread - the fourth - has reached the (arbitrary?) 500 comments threshold, so it's time for a new thread for Eliezer Yudkowsky's widely-praised Harry Potter fanfic.
Most of the paratext and fan-made resources are listed on Mr. LessWrong's author page. There is also AdeleneDawner's collection of most of the previously-published Author's Notes.
Older threads: one, two, three, four. By tag.
Newer threads are in the Discussion section, starting from Part 6.
Spoiler policy as suggested by Unnamed and approved by Eliezer, me, and at least three other upmodders:
It would also be quite sensible and welcome to continue the practice of declaring at the top of your post which chapters you are about to discuss, especially for newly-published ones, so that people who haven't yet seen them can stop reading in time.