I’m not sure this is possible since 4.5 does some hardware update so you will not be able to go back to 4.4. Besides, even if it is possible, it may carry over all issues you have, and will not answer the question if there is an issue on fresh installation of JetPack 4.5.1.
What this means, if for example you try fresh 4.5.1 JetPack installation on another SD card, your SD card with 4.4 will no longer work with upgraded Jetson Nano. So this makes sense only if you want to migrate to 4.5.1. But since JetPack 4.6 may be released soon (according to VisionWorks will be retired after JetPack 4.6.x, JetPack 4.6 is targeted for Q2 2021), migrating to 4.5.1 probably not worth the effort at this point (unless you really need it now), and it is better to wait for 4.6.