No, there's absolutely no reason to treat a question differently if a user has been blocked from asking questions on a particular SE site.
If a question isn't a good fit here on Programmers, here's a good workflow:
The first thing to look for is questions that aren't a good fit anywhere. If it's primarily opinion based, too broad, or unclear, it's highly likely to be those anywhere in the network. Some communities may be a little more lenient than others, but they are generally applicable. Use one of these reasons if it applies.
If the question is off-topic here, but on-topic on a site that we have a migration path to (currently only Stack Overflow), you should vote to migrate that question. If the user is question banned, the migration will be automatically rejected and the question will be closed here anyway.
If the question isn't on-topic here and isn't suitable for migration, use one of the custom off-topic reasons. We currently have three - career or education advice, writing/debugging code (that doesn't meet the SO minimum guidelines and isn't suitable for migration), or recommendation.
If there's anything else wrong with the question, use a custom close reason. Most of the questions should fall into an existing reason, though.