Yes. A Format operation only operates on the ONE Partition you specify and does not touch the other. That is, of course, if you really mean FORMAT, not re-partitioning. Don't know about you, but I see a lot of confusion over this on these forums.
There are two types of operations necessary to prepare a new blank disk for use by any OS. And each of them can be re-done later. The first is Partitioning, which creates a table at the start of the disk detailing how the disk's space is allocated to regions called Partitions. There MUST be a Primary Partition which can use any amount of space, right up to all of the disk. Then there can be one or more additional Extended Partition(s) if the Primary left some space Unallocated. Each of these Partitions will be assigned its own unique letter name, and treated by the OS as a separate drive. Then, for each such drive (Partition) the space must be Formatted to establish the File System being used on it. This creates within that drive the hidden data tables for tracking the actual use of space within that one drive, but it has no info about any other drive (Partition) on the physical hard disk.
Once the Partitions exist, each can be re-Formatted if necessary without doing anything to other Partitions. A Format will essentially delete all data on that one drive (well, usually it just erases all of the tracking info and starts with blank data in the hidden files). On the other hand, you also could re-Partition the drive. That is, you can Delete a Partition which will completely destroy all its information. You can create a new Partition from Unallocated Space, but all the space you use MUST be contiguous. Any new Partition will need to be Formatted after creation.
So, if you really mean not to make any changes to the Partition structure of the hard drive, but just to Format one Partition, it will NOT touch anything outside that Partition.