It could be the case as you say but still you can test if the globalprotect options will not terminate the RDP "User Switch Tunnel Rename Timeout" also check if this option is enabled "Enforce GlobalProtect for Network Access" as if the VPN is not up the globalprotect will block any connections till the VPN us up and this caused me a lot of issues in past. Outside of that maybe raise a support case.
Also maybe check the split-tunnel option in the globalprotect configuration as the below article seems to match in some way your issue "Why Does a Local Client Device Break RDP Connection to Cloud-VM Platform when Connecting to a GlobalProtect Gateway?":
Globalprotect 3.1.6 Download
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