Maybe, maybe not.
'When I accelerate, the joint opens.'
Pretty much ALL FWD cars have the engine move ROTATIONALLY up to one inch easily in mounts and why they have flexpipes built into the headpipe to allow that movement. Depending on mount geometry the pipe may move around quite a bit and what allows the leak, the exhaust pressure by itself like said is way too low to do that.
When you accelerate the pipe can move around hugely and normal unless something is broken. My Ford Focus cars you can go to the back tailpipe exit and move the entire pipe to the engine up to 4 inches and normal to allow for engine movement under load.
There is no mentiioned evidence of lost performance from a clogged exhaust that I see.
Upon further looking at the pic I see that headpipe appears to positively be contacting the opposite sealing flat on manifold and that is INCORRECT, any seal or gasket should be bumping the headpipe down a bit to not touch and why it is leaking too. Maybe wrong size doughnut or other part there. A normal install has the two major meeting parts spaced apart so any seal between them can work. With the major parts touching then any movement in pipe translates into a jacking force on the lower flange to move it and the meeting flat apart to leak. Touching also means the seal is leaking as it is not properly compressed.