IMO, no. MH displayed behavior sufficiently bizarre to justify his admission to a psychiatric facility for the protection of himself and others. I don't believe there's any requirement that a specific diagnosis be made within a brief timespan but that it's enough to note the behavioral abberation. Besides, the police themselves have stated that MH has been "cooperating" with the investigation, even though they've also stated that he's not told them the truth. They haven't been denied access to him and my guess is that they are probably pleased that he is under wraps like this. It simplifies things for them and they don't have to worry themselves about his doing anything frisky, such as murdering potentially incriminating witnesses or further tampering with evidence.
I'll bet Mark won't be staying in that hospital once the arrest warrant is issued.
I suspect this is more a matter of laying groundwork for his defense, although it must also be said that anyone who lies as much as he has over the years--and thinks he can get away with it forever--can't be quite "all there."