Chopped up into parts:
can connecting multiple HDDs increase throughput?
Yes. RAID is usually the answer, or multiple used filesystems spread across several drives.
(spinning simultaneously as RAID JBOD)
JBOD is 'just a bunch of disks' and henbce it is not RAID.
Did you mean to write RAID or JBOD?
to a single SATA port
A single SATA port usually only connects you one device. Yopu can not connect multiple SATA drives directly to a single SATA port. There are ways around this by using a port multiplier. In case you your SATA port talks to one disk at a time. It can switch to another disk and it can do so quite fast, but it is still talking to one disk at a time and you will quickly saturate this link if you cannot 3 or more disks.
Also the motherboard (or rather the used SATA controller, which usually is part of the motherboard) needs to support this.
Is there a specific reason why you asked for one SATA port?
Traditionally one either uses faster drives, or connects multiple drives to an equal number of SATA ports. Or one usues a dedicated RAID card.
SATA II supports 375 MB/s read/write speed.
Not in practice. 270MiB/sec is about the max which is archivable on SATA-II.
Note that 33.0 gigabit/second includes the bits used for protocol overhead. Actual data transfer is a lot lower. The 270MiB/sec was archieved using a fast SSD and using the SATA controller build into the ICH9/ICH10 chipsets. Other controllers usually usually slower.