External collaboration without doctoral supervisor - is it a fair request to pursue this?
Your advisor doesn't own you, so yes, in general you can pursue other research collaborations. 

However, there are situations in which the answer would be otherwise. If you are in a lab science (or similar) in which you are depended on and this would interfere with the work of others, then you have to cover your obligations. 

Since you mention funding as a tag, it may be that you have a grant that requires full time attention to the work of that grant. That might make it more complicated. 

The personality of the advisor might make it inadvisable to do this prior to finishing your degree. It wouldn't be right to forbid you to do this, but it could happen.