It will in combination with a scrapper like www.amazon.com/Titan-Tools-12031-Razor-Scraper/dp/B000OEDQQW
Rubbing alcohol on a paper towel, rub down the surface, scrape the glass then another round of alcohol. It should leave you with a perfectly clean surface.
I always use a mixture of half vinegar and half Dawn to clean the shower door. It's basically known as a homemade degreaser.
I've never let it sit for 30 minutes, but I have also never seen a shower as bad as the one in the photo...
To really help with stubborn mildew and soap scum, you should invest in a razor scraper. I personally use this one, and it's great for glass, mirrors, windows, stovetop, etc.
Make sure you get a single edge razor scraper too, like this. Honestly it's far more useful than abrasive cleaners in getting baked on gunk off.
You can use that, and then finish it up with a little baking soda (wet it slightly to make a paste) and never buy cooktop cleaner again.
Carefully use a razor blade scraper. Make sure you don't pull any fingers in the way, I use steel blades, but you could use plastic blades.
I use the same for both, flat edge razor/scraper.
Something like this one:
https://www.amazon.com/dp/B000OEDQQW/ref=cm_sw_r_cp_apa_i_w4VtFbQA6FH1D
Use an unused single edge razor blade, and be very careful. I recommend getting a holder for it for maximum control.
Get one of these http://www.amazon.com/Titan-12031-Mini-Razor-Scraper/dp/B000OEDQQW for scraping off the old caulk. Also, make sure that you really dry the area before applying the new caulk or you'll have a bad time.