No, it wouldn't. The riddle stating "so that if you drop a match on it" means the action of dropping the match on the paper must be responsible in some way for one to see flames.
If the match being dropped had to cause the flame, it would read "if and only if a match were dropped on it".
But dropping a match is not the cause of your friend lighting kindling.
Outside the box answer:Spoiler for b
The match is not being dropped on the paper in either of those examples.
You could cover it with a thin sheet of metal, or any other nonflammable solid that completely covers it, then a second piece of paper, and drop the lit match onto that.
You could put it at the bottom of a bucket of alcohol and drop the match on that. You would definitely see flames, and the paper wouldn't burn for a long time
Again, the riddle states that dropping a match on the paper will be the cause of flames to be visible.
mabey you could drop an unlit match on a piece of paper an look at a fire