Would it be better to be vocal and ask for more time to think about
the offer when I have been given it? What happens if it isn't in the
foreseeable future that I would be able to accept the offer? (i.e.
While anything is possible, as a hiring manager I can't think of a time when I would have held a candidate's position for a period of months. That's particularly true if the reason for the delay was "too many things going on in my life and thinking about relocating". Those are likely both red flags for hiring managers.
Let's say I did end up rejecting the offer and I wanted back in. Would
I reach out to my recruiter and/or the manager?
When it happened with me, I called the hiring manager.
Overall what exactly is the process for hiring someone who previously
turned down an offer? Are they even considered?
Every company is different.
Usually, if the position is still open, you could indeed be considered. But sometimes managers feel that they were rejected, and thus wouldn't re-consider. Other managers wouldn't trust you, feeling that you changed your mind once and might change your mind again, and thus wouldn't reconsider.
To be re-considered, you would want to have a great reason for declining originally, and good explanation why things are very different now.
In my case, I declined an offer (because I felt that the position wasn't quite the fit that I was looking for). I got laid off two weeks later, and called up the hiring manager to ask if I could be re-considered. I was, and I got hired. I planned to give it my best try to make it work. But my intuition about the company proved correct, and I ended up leaving within 2 years. For me, it wasn't a career highlight.