Nope.... best is to use a 2.5 to 3.5 form factor convertor for allowing you to place a top quality SSD in the SATA port 0 drive bay of the Z620. That conversion and more is described in detail in this post HERE. The port 0 bay is the bottom one of the three in there.... 0, 1, 2 is stamped in the metal, hard to see unless you know, on the left side of each bay in your Z620.
Unliike with the Z600 (a SATA Gen II workstation) the Z620 can utilize the added capabilities of a SATA Generation III SSD just fine, and you can read up in Anandtech.com for their current recommendations on the best SSDs as of Q3 2016 HERE.
http://www.anandtech.com/show/9799/best-ssds
The Z620 does not have a M2 slot. You will get yourself to near perfection with one of the top SSDs noted in the article above. If you need more there is more... the HP Z Turbo Drive that you can research on, but that is not the "best" option for a boot drive in my opinion. Depends on how you define best.....
Make sure to update your BIOS first.... 3.90 is the latest. You can reformat that original drive and use it in the SATA bay above your port 0 bay as your documents/storage drive. I can send you my optimized Z620 BIOS settings for import after you have done that (you can clone in BIOS settings via "Replicated Setup") if you want.... PM me via the forum with your email address. It is a small CPQSetup.txt file, and you can import that from within BIOS.
Regarding W10.... hopefully the Z620 came with a W7Pro64 install. I believe you can still upgrade to W10Pro64 for free if you are disabled. Virtually never will a used HP workstation come to you with the original drive and the Recovery partition intact/unused, but if it does for this one make sure to capture the HP Recovery media onto a thumb drive first.