Simply put, if the designers of a new language want it to gain adoption and interest from the largest group of programmers possible, should those designers build a highly productive(Intellisense like features to begin with) IDE to encourage the adoption of a language?
No, the IDE should not compensate for the language's deficiencies.
Having said that, the IDE sells VB to customers of mine all the time.
So, a fancy IDE tends to sell a language. Even though it shouldn't.
In a word, no. How many IDEs were built for HTML? Javascript? Ruby? PHP? etc. All of these had the language come first, and the IDEs come second.
I think it's great having a good set of tools to help productivity but it's not a 'should-have'.
Yes.
Even if you've created the most useful, most advanced language on the planet, there's no way I'm going to waste my time coding in it if I have to use notepad.
It's in the best interest of adoption to have tools available that are accessible and can automate much of the overall process. The less time it takes to do something, the more time can be spent on actual development.
Cost for the IDE is the other factor that will affect management buy-in. Some places are OK with the write-off, most would prefer to keep overhead to a minimum.
The syntax of a new language can mostly be learned in a few hours. What takes most time and effort is to get to know the APIs. To have a good IDE with IntelliSense makes it so much easier to poke around and learn the APIs than looking up in documentation.
In an environment where developers are used to good IDEs it is harder to advocate the use of a new language if some of the IDEs people are using lacks support for the language.
E.g. on the java platform there is a lot of new languages that could be used in conjuction with Java, like Groovy, Scala, JRuby etc. Up to now it has been a problem if you want to start using Groovy and some of the developers use Eclipse, because the Groovy support in Eclipse hasn't been that good (luckily that is changing right now).
I'll say "yes." If not the productivity of, at least the presence of an IDE will bring in IDE-lovers and is unlikely to discourage command-line or Vim enthusiasts.
If not a full IDE, at least syntax coloring.
Evidence: Fully half the SO questions tagged Objective-J ask about syntax highlighting.
History shows that the language comes first and the IDE follows. Instead of building an IDE, build the killer app (Unix, mobile code, Rails, ...).