Hello ERM-Consulting,
OpenVPN can break Internet connectivity if things are not configured properly. Normally with a split-tunnel configuration, the Internet access is left totally untouched on the device, and only specific subnets are routed through the VPN tunnel. My guess would be that you're maybe pushing a DNS server that just doesn't work for Internet addresses, and thereby could possibly break things.
Without more details it'll be hard to determine what exactly breaks. Perhaps it is best to post log details at
https://openvpn.net/support so we can analyze that without having to post such details on a public forum.
Kind regards,
Johan