I can't make that guarantee. I don't know your VLAN structure and what is the root of each VLAN.
A Cisco 4503 can use PVST and RSTP, which maintain per-vlan spanning tree instances. The rest of the industry, including Cisco Meraki, don't do this. They use single instance.
So yes - it absolutely can cause issues.
mst on the other hand uses defined instances - and by default that is a single instance. mst is also compatible with PVST and RSTP as well.
mst is the safest choice.