Reinstall OS on primary node in cluster

This should not be a problem. After "clusterization", there is no first node anymore. I could only imagine problems if the name stays the same.

Best to try it yourself: install a test cluster inside your real cluster. Then you can test upgrades and also this kind of "what happens if"-stuff.
 
I have some small problem with cluster on proxmox 4.

First story: when we create cluster https://pve.proxmox.com/wiki/Proxmox_VE_4.x_Cluster
we do
hp2# pvecm add IP-ADDRESS-CLUSTER
where IP-ADDRESS-CLUSTER it's ip address first node on cluster.

can I reinstall first node on cluster and add this node to ip address on second node in cluster?
You can have problem if your new node has the same name that the removed, you can work with old ip, but you must change hostname.(this worked for me)

if you want work with old Ip and Old Hostname you must do the procedure :Reinstall Node cluster (i tried this and i couldn´t reinstall my node cluster). :S

https://pve.proxmox.com/wiki/Proxmox_VE_4.x_Cluster
 
It might be interesting to you to work with clonezilla for backups, =)

I would suggest to use ZFS, which is able to do online snapshots and therefore backups. Proxmox has included a lot of helpers around ZFS and off-site replication. You can even create bootable backups by using ZFS. This allows very fast disaster recovery.