First your premise that they won't "by trying too hard to detect a fake":
As some one who has had a lot of CTs and MRIs: they may not find minute damage (esp. to axions) in patients who have brain injuries. However, they will do a CT & MRI right away and probably several different ones. This is because they will need to rule out bleeding in the brain and other life-threatening conditions as 20 to 40% of patients with this acute an injury dies.
Basically, they are going to look hard at the brain of someone unconscious for a few hours let alone days because this would indicate a severe case of TBI.
Now back to the, can you fake TBI for a little while:
To quote the American Society on Neuroradiology on Traumatic Brain Injuries (emphasis mine):
Magnetic resonance imaging (MRI) is a powerful diagnostic tool that can detect signs of injury such as minute bleeding (microhemorrhage), small areas of bruising (contusion) or scarring (gliosis), which are invisible to the CT scan. Newer, specialized types of MRI can assess brain structure at an even finer level or measure brain function to detect alterations in brain structure and function due to TBI. Because microscopic injury to the brain may be a cause of problems, however, even MRI may not be able to detect any abnormality in a patient with TBI.
So can someone fake brain damage? Possibly (may even just get misdiagnosed in a situation like you give where "brain damage is expected"). However, in your case, this would not be a mild form of TBI (unconscious for weeks = acute) so the lack of this evidence in an MRI would probably start doctors looking at other things (with "cures" which will cause bad things to happen to your character due to side-effects or just not having the condition).
Can you fake it for weeks in a vegetative state?
Again, its your story, so doctors could miss all the signs and a vegetative state is not a coma so you can respond to stimuli. So its possible for at least a bit.
However, the difference in reaction from a person with TBI and a "normal" individual can be striking and a good ER will be used to seeing these differences. For instance, even if you take medication which makes your person not react to smell in any fashion because he is faking the reaction people with TBI may have (when injuries include the nerves from brain to nose being cut so don't have a sense of smell anymore1) its may be hard to fake these within an MRI when their testing your reaction (the sound and lights of the MRI themselves can immediately show different reactions then expected within a person with TBI's brain 1).
To further point out how hard it is to fake TBI for a long period (for your story but also because I don't want people to think there isn't ways to detect it), see the rest of my earlier quoted statement:
Long after the injury, MRI as well as CT may demonstrate brain atrophy, which results when dead or injured brain tissue is reabsorbed following TBI. Because injured brain tissue may not completely recover following TBI, changes due to TBI may be detectable many years after an injury.
So there's going to be a point where the doctors say "this isn't caused by brain injury. What are our other options?". I would put that point at 2 days over 2 weeks but it is possible that a misdiagnosis or other story reason extends this and when coming out of the state the doctors just say "well, we'll have to follow up and see if we see the other indicators as he is doing better now". Probable? no. Possible? there's a lot of malpractice cases for a reason.
1: personal experience