Yes a 3G SIM will work in a 4G phone. You will only be able to access 2G and 3G services, so the system will be slow and some services on the 4G phone will not work because of insufficient bandwidth and speed.
Most service providers will be happy to upgrade a 3G contract to 4G because they will anticipate higher earnings as you will be using more data and paying more for the service.
If you buy a phone with dual SIM capability, you can have a pay as you go 4G SIM alongside a 3G contract SIM, with two different services and two different numbers on the one phone. Of course the 3G restrictions would still apply when using that SIM.