"Are you planning to move to China?"
You can't just say 搬: "你们打算搬中国吗?" doesn't make any sense to many native speakers. That being said, some northern dialects may say it this way, especially when the context of the conversation implies moving (house/home).
The character 去 in here is an adverb indicating the direction/consequence/end result etc. of the verb 搬。
The above English sentence can be translated in several ways, but an adverb cannot/should not be omitted:
你们打算搬去中国吗？(asking outside of China)
你们打算搬到中国去吗？(same as above)
你们打算搬中国去吗？(same as above 2 but more informal, colloquial)
你们打算搬来中国吗？(asking within China)
你们打算搬中国来吗？(same as above but more informal, colloquial)
你们打算搬到中国吗？(asking in anywhere)
你们打算搬中国到吗？(WRONG!!! doesn't make sense)
搬 is actually shortened from 搬家 move house/move home/relocate. Therefore you can use 搬家to replace all 搬 in the above example sentences.
搬 on its own, without 到/去 to indicate context and direction, simply means "to move, to lift, to transport, to shift (position)"。
In summary, 你们打算搬中国吗？is okay-ish, but not recommended.