I'm afraid that would likely end in disaster, sorry. 8/
Assuming your tank isn't an NPT, even if you have managed to cycle your 3 gallon, because cycles can be less stable in tanks under 5 gallons, that Platy will likely throw off your parameters(they can be a tad messy, if I remember correctly) and mess with/possibly crash your cycle.
If you HAVEN'T cycled your tank and you don't even have a filter, the platy won't survive. They need cycled tanks with filters and oxygenated water, which is something bettas can only get along without because of their Labyrinth organ which allows hem to breath air from the surface.
On top of the bio-load/possible lack of filter issue....3 gallons isn't a lot of space when you think about it. Perfectly fine for a solo betta, but bettas are an aggressive and territorial species....is very likely the Platy would be attacked with such limited space.
Sorry, but its just really not a good idea....