I think you're (implicitly) asking three questions at once, so I'll address them individually.
The question in your title
Q: Is it possible to search sister SE sites before posting a question?
A: Yes
Honestly even if you were on the Webmasters site your question may not have pulled up the one we linked you to. The Stack Exchange site-search is pretty awful - you should always ask Google first (considering it is basically the sum of all human knowledge these days).
That said, even Google fails sometimes - there's nothing wrong with googling, not finding what you need, and asking anyway. The worst thing that can happen is your question gets closed as a duplicate (or "off-topic, go look here instead").
It would indeed be nice of asking a question on one SE site searched all related SE sites, but that idea has two major problems:
- What is a "related" site? (nobody is going to want to curate that manually), and
- Search is HARD
(If you want to raise that suggestion on mSO you can certainly do so, but it's probably already been suggested and shot down. mSO is also not the most hospitable part of the Stack Exchange network...)
The question of topic fragmentation being harmful
This has been brought up and debated to death many times. A lot of us feel topic fragmentation is a Bad Thing, myself included (if you think Webmasters has a lot of overlap with Server Fault consider that 100% of unix.se is covered by Server Fault and Super User, which both existed well prior to unix.SE).
Unfortunately the net consensus is that specialization trumps fragmentation.
Maybe one day we'll reverse that.
The feature request to allow the community, as well as the moderators were able to exert some say on whether questions are right for a particular forum
Is status-completed, status-bydesign (through the Reputation and Privileges system).