First, I use a lot of Minwax Polyshades which has the stain and varnish in one can and only as many single applications of both as you want to apply. This dry filling may work with stains, but it works really well with the Polyshades and I'll explain why in a moment.
I keep a supply of wood dust from my spruce and pine to make filler, so my sander dust collector was empty when I started sanding my oak wood and plywood. After joining the front edge and backsplash on my counter top, I could see a tiny gap running across the front. I sprinkled oak wood dust from the sander along the gap and rubbed it in. As it settled, more gaps appeared, and I just kept rubbin in more dust. When I wiped the piece down for spraying, I was careful not to wipe out the dust.
After spraying the first coat of Polyshades, the varninsh in it helped the dust "stick" in place and the dust accepted the stain and was almost undetectable. When I sanded for the 2nd spraying, I saw a few places where the dust didn't stay put, so I rubbed in more dust and made the 2nd spraying. After that, no gaps were visible, and there were no tell-tail, lighter than the wood filler marks. Now, I am ready to sand and spray on a couple of coats of clear gloss.
Here is a before and after filling and staining picture of the same area on my potty cabinet top. Where the two pieces of edge wood join, I didn't get enough dust in the crack, it's my fault you can see some space there, not the fault of the process. Also, it looks like the wood in the after wasn't stained, but that's the fault of the lighting when I took the pictures, and the stain is very light as well.