I plan on installing a secondary hard drive (1TB?) in the optical drive bay. I heard that drives can become bottlenecked when installed there because of connection speeds. Is there any way to upgrade the connection speed?
No, but even if it is only S-ATA 1.5 Gbps (S-ATA I) as interface, that is fast enough, as platter based HDDs will not even saturate S-ATA 1.5 Gbps (S-ATA I).
HDD sequential read/write speeds are between 75 to 125 MB/s, depending on the drive, a 1 TB 2.5" HDD will probably be around 85 to 100 MB/s. S-ATA 1.5 Gbps (S-ATA I) offers around 148 MB/s.