There are two aspects you have to take care of, Azure itself and Fortigate licensing.
The upscaling in terms of the VM on Azure should not be a problem at all, if you're scaling within the same VM size family (example D4s_v3 to D8s_v3). This is usually done within seconds rather than minutes.
Talking about Fortigate, according to the following link, there are two license types available... Bring your own license (BYOL) and Pay as you go (PAYG).
In your scenario, I'd recommend to use the PAYG option, so you do not have to care about the vCPUs licenses for Fortigate, as this will be charged as you go, just like the name indicate. If you chose the BYOL option, you have to take care yourself to cover all the vCPUs accordingly, as far as I interpreted this correctly.