Not in the slightest. We have demonstrated interoperability in Afghan and Latvia with our allies. We are competent soldiers/sailors/aircrew.
Our main problem is a lack of equipment. I have no problem seeing a section of Can Infantry GIBing in a Bradley or a Canadian Crew in augmenting on a UK destroyer.
I don't think you'd see Cdn soldiers in a Bradley commanded by US Army NCOs/Officers.
I could, as a minimum, see Coy or equivalent sub-units attached to Allied forces. Why Coy level? That would put them under the "command" of a Major. Something about "Senior Officer" sounds right to the public and elected officials.
I don't see lower than that for conventional ground forces.
Comparatively, that is basically what happens when "my kind" go off to do things; we form an Air Task Force (even if it's only a 1-airframe Det) under a Maj (minimum) as the ATC Comd. We are under Cdn command & ROE, always, regardless of where we plug into the overall formation.
I think the same rank delineation line exists in the RCN; IIRC, MCDV skippers are LCdrs.