Yes. Most cloning software will let you copy partitions, in addition to cloning the entire drive. I'd suggest doing it the following way:
Copy second partition on old HDD to new HDD. Expand partition size on new HDD if needed.
After you verify you have a good copy, delete second partition on old HDD.
Clone old HDD to SSD. Cloning will make sure all the necessary boot files and partitions are copied as well.
A straight up reinstall on the SSD is always best though. If you clone, you'll have to manually go through and change a bunch of settings for the SSD (e.g. turn off disk defragmenting, superfetch, enable TRIM, etc.). When you do a clean install, the installer detects the SSD and sets most of these automatically.