It would be possible but you would need to add your AMER routes onto your on-prem EU Route-based tunnel and also include your EU on-prem routes in your BGP tunnel
Additionally, you must add GCP Firewall rules in order to allow traffic between those 2 GCP tunnels
You should be able to communicate between your on-prems as long as your on-prem hardware has the appropriate routes / firewall rules
Keep in mind that there's no natting here unless you implement a 3rd party solution
Edit: I replicated this to a certain extent (as I don't have your on-prem hardware or physical locations), my AMER and EU on-prem consist of different GCP projects to simulate this).
I have the following topology:
on-prem AMER <-BGP-VPN--> GCP <-Route-Based-VPN--> on-prem EU
I have added the needed GCP Firewall rules to allow this and I defined the EU route onto my GCP BGP session as this is not done automatically, but it's possible to ping from AMER to EU.
At this point it would be better to reach out to GCP support in order to look specifically in your GCP project (expect being asked for packet captures on your on-prem hardware), but if this is a on-prem config issue then it would be better to reach out to your hardware support in order to configure this.
Images:
