Do I need a cellular capable iPad to use ForeFlight Mobile?

No. However, the cellular-capable iPad is needed if you want to have a GPS receiver built into the iPad. If you get a WiFi-only iPad, then it will not have a GPS receiver built into it. The moving map and geo-referencing functions require a GPS source. If you have a WiFi-only iPad, then you will need to use a portable or panel connected GPS receiver. 

Charts should be downloaded over WiFi since the data can be significant in size. If you do have a cellular-equipped iPad and a data plan, you can use the cellular data to check the weather, file flight plans, etc.