Can the Cisco 3650 do the job of distribution/core layer?
We have at least 250 devices that will be connected to the network.
More info :
The Cisco 3650 is needed for inter-vlan routing.
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The 3650 will switch layer-2 at wire speed, even if you have it fully populated. You cannot get more traffic into the switch than it has ports.
When it comes to routing, there are too many variables to answer with the little information you have provided. Certainly, any configuration which causes the routing to be process switched will severely impact performance.
A problem you will have is the access to distribution bandwidth ratio, but this will be a concern with any distribution switch. You don't say over how many access switches the user will be spread, but let's assume six 48-port access switches connected to you distribution switch. That gives you just over 40 users per switch. If the users ports are 1 Gbps ports, that means that you should have, at least, 2 Gbps uplinks from each access switch to the distribution switch in order to meet Cisco's recommendation of a 20:1 access to distribution bandwidth ratio.
The next bandwidth ratio you need to worry about is the distribution to core bandwidth ratio. Cisco recommends this be no more than 4:1. For each 4 Gbps bandwidth coming into your distribution, you need at least 1 Gbps from the distribution to the network core.
Whether or not a 3650 will meet your needs depends on how you configure your network topology, and what sort of routing controls you use, but it could work in some cases with 250 users. I have seen the Cisco 3K switches used as distribution switches for a lot more than 250 users with no problems. You just need to carefully plan the use.