The answer is: probably. The "loose" part of this is that the Free Space available on the formatted SSD would have to be slightly LARGER than the full size of the 320 GB HDD to be sure it would work.
But I have two questions:
1. Why back up a HDD to an SSD? The opposite direction is much more common. A backup is made once and then stored for use later. An SSD's strength is it is VERY fast for data access, BUT very expensive. So why use such a device for storage of data you HOPE you will never need?
2. Your original question was how to back up a 1TB unit to a 320 GB unit. So, is there any data on the 320 GB unit you need to save via backup? If so, how did you plan to fit more data onto it from the 1TB unit?
A complete image of a HDD is useful for some things, but not necessary as a backup. The image includes ALL space on the source unit, whether it contains useful data or not. A Clone copy also does something similar if it it set that way. But a true Backup includes only those areas of the Source unit that have data stored on them, so the backup volume usually is less than the full size of the source unit. However, backup software often gives you the choice of making a copy of only those areas, or of making a complete image, as you had planned. To make an image, your Destination unit MUST be at least as big as the Source unit.