Is it possible to connect a VLAN switch into a dumb switch ?
The router will know how to reach network connected by a VLAN through the dumb switch please ? No edge effect ?
By example, a schema of the project :
An unmanaged switch will only have one VLAN. Some unmanaged switches will drop tagged frames as damaged, others will strip the tag, and some will simply pass the frames unchanged. Unless you try it, you have no way to know how your switch acts. For the switches that strip the tags, all the frames will be placed into the native (untagged) VLAN as they pass through the switch.
If your VLAN switch is a layer-3 switch, then you are better off using it as the LAN router and creating a routed link to the router, which can act as the WAN router. You will need to either use static routes on the WAN router, or you will need to run a routing protocol between the WAN router and the layer-3 switch as the LAN router.
Yes, you can do what you're suggesting without any problem.
In practice, the dumb switch treats everything as if it's on vlan1. Technically though, vlan tags are removed when leaving access ports and applied when entering. Vlan tags are only kept in the frame between switches when crossing a trunk port. Since you're not creating a trunk between to the dumb switch (or router), then vlan tagging is not an issue.