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.