Is this little pipe the answer to the running issues on my 2005 R53 Mini Cooper S??

I've bought a 2005 R53 Mini Cooper S from Copart with the description stating it had a undiagnosed noise from the engine bay. After getting the car, I quickly discovered a very strange noise on lift off and a lack of power. After a bit of research, its pointing towards the timing being out, so I previously changed the timing chain, serviced the supercharger, replaced various gaskets that were leaking and in my last video, I looked to see if the catalytic converter was blocked. But none of these fixed the issue. So, after watching a video on YouTube where someone had a lack of power on a R53 JCW, they finally, after 6 months, fixed the issue. When looking at the comments to their video, a lot of people had fixed various running issues after seeing his video and it was down to this little pipe coming off the intake manifold. Fingers crossed! The silicon vacuum hose was purchased from: https://www.amazon.co.uk/dp/B019VZJNS...