No. The point of the 5 min all out on the test is to better estimate your 20 minute power. Those with higher anaerobic abilities can use those abilities to get through a 20 min effort and end up with a higher estimated ftp number than those more aerobically inclined. Hitting that 5 mins all out forces everyone to rely more heavily on their aerobic fitness for the 20 minutes.

Trying to do that before a workout is going to kill your workout. A true 5 minute max effort will leave you struggling to complete one 20 minute effort, let alone two.

So yes, it will hurt and no, you shouldn't do it.

Doing a couple of minutes at ftp or slightly above to ensure you're properly warmed up is generally good, though.