Can I connect SATA drives to SAS connectors?
Yes, well known question / answer
Does the 6 Gb/s transfer rate means that I'll get an equivalent of SATA 3 (which is important if I use SATA 3 SSDs)?
Yes. They will negotiate the speed, slower device wins (12G sas ctrl will lower speed to sata 2 drive if needed) or drive will lower speed to older SAS controller. MSM software (or BIOS) can show you negotiated speeds.
Are there drawbacks using SAS connectors instead of SATA 3 ones for SATA 2 and SATA 3 drives? In other words, if the motherboard has both SATA 3 and SAS connectors, what is the reason, if any, to use SATA 3 connectors for SATA drives?
Use SAS. Usually SATA connector are part of Intel southbridge. Tests I've done show throughput drops proportionally to number of SATA drives connected to southbridge and results were horrific for 6 drives used simultaneously on Intel southbridge.
SAS controller on your motherboard is probably LSI using 4 pcie lanes - throughput was the same if you use 1 or 12 SAS drives (i lost the link to that blog I made).
Yes you might have to buy appropriate SAS cable (it's another topic, cheap on ebay from china).
The only reason where you might not use SAS is when BIOS doesn't allow booting from SAS drive (but todays everyone boots from NVME anyway).
Here is a test of my SAS setup, 16 drives on expander (expander slows things down, but results are shockingly better than you would achieve with intel southbridge).
Simultaneous test of 6GB eMLC on 12GB controller + 24 port SAS expander. Doesn't matter if drive is sas or sata.