Can I restore from a time machine backup after doing a clean install?

Short version: Either the SSD or drive cable has failed in my early 2011 MacBook Pro. I plan to swap in a new SSD, do a new macOS install and use the device for a day to make sure it works fine before I connect my external hard drive with my time machine backup to restore from. Is this something I can do? Will there be any issues ?

Long version: the symptoms are MacBook switches off after apple logo appears. Original hard drive died in 2017. I replaced it and that died a few months later then replaced it with a ssd Samsung 850 evo in 2018. Worked fine since aside from a crash or two.

I’m intimidated by the cable swapping process. I feel like if it isn't at fault I may damage it swapping it out and cause further problems. Hence why I just want to swap the SSD only and test it out. I also don't want to restore from my backup straight away in case it somehow corrupts my only backup as my current SSD has corrupted. I only want to connect my backup if I am 100% certain the MacBook is working fine.

I plan to swap ssd then let internet recovery complete then via disk recovery and disk utilities, reformat the SSD and then install whatever recommended macOS. Test the MacBook by closing opening, switching on and off etc. If all is fine THEN enter into recovery mode and restore from backup.

I want to make sure this is actually doable and I haven't over looked anything. Will there be any problems?