Given that this is the more constructive version of your other request, here are my thoughts.
Answering the title directly:
Can an account be self-suspended?
An account can't technically be "self-suspended", in that you don't have the ability to give yourself a suspension. Suspensions are handed out by diamonds. So in the most literal sense, no, you cannot.
Answering the question body directly:
Is it possible to obtain a suspension on one's own user account by request?
Yes, this is completely possible. As Fabian points out, this requires various degrees of diamond and/or SE dev work depending on the scope of the suspension.
However, I firmly disagree with Fabian on the following statement (and this is just me, as a moderator on Stack Overflow, I'm not speaking for the other moderators on Stack Overflow or on the other Stack Exchange sites):
so I think most moderators would agree to your request and suspend you, if you wish so.
Personally, I would not honor this request.
This is something we're simply not qualified for.
This isn't to be confused with a lack of empathy for a situation where one would want this, but there's too much liability (in as much as we can have given what we do, really) attached to an action such as this.
If you feel that there's a compulsion to be on or a reason you feel you can't be away from Stack Overflow under your own will, then that's a behavioral issue, and that's an issue for you to deal with. We are not behavioral therapists.
To even begin to approach that role would be extremely negligent on our part and could possibly do you more harm than good.
Finally, there is the canonical reference on suspensions originally written by Jeff:
Nowhere in the post does it indicate that a suspension is to be used for users who are constructive to the community. From that post (emphasis mine):
Our general strategy is to discourage specific problem behaviors, not
individual users. But sometimes you just can’t seem to reach people,
and it becomes necessary to place accounts in timed suspension.
Quite simply, you aren't exhibiting problem behavior (and I don't encourage you to do so for your purpose) and as a result, you don't fulfill the requirements for suspension.