No you do not need any downtime to do this work.
But be careful before changing this. Make sure all your Storage network(network interfaces, switches, ports, etc.) have the same MTU before you changed. If not, doing this on production if they are not aligned you will have issues with the datastores.
But changing MTU is at Virtual Switch and Port Group and vmkernel. Check all the paths.
But if were me, I will put the ESXi host in maintenance mode before I do those changes.