When a VM needs external internet, it goes through 'Switch 1'.
=> Yes, you could.
When a VM needs internal internet (e.g., for clustering, HA), it goes through 'Switch 2'.
=> Yes, you could
If 'Switch 2' fails, then it should switch to using 'Switch 1' for internal internet as well.
=> Technically this is possible, but you have to change your setup, and draw different picture than your current one.