Yes, because it allows more time for coffee to be extracted as it stored in a longer time for coffee to drip. However, other parameters also have effect regarding this issue (such as, type of bean, roasting profile, temperature, brewing method)
But using double filter since it also filter the "flavor", making it stale (you may lose the pleasant acidic, fruity flavor, or other unique flavor your bean may offered) and double filter can make your coffee over extracted thus unpleasant bitter flavor.
If you want your coffee strong you may want other experiment
- Use fresh coffee bean
the older the coffee, they tend to lose their flavor. The fresher, the better. You have to store your bean properly too, keep it in air-tight container, avoid direct sunlight
- wait to grind your bean, until the last minute coffee lose a bit of its flavor after grinding. Ground coffee is also more sensitive to the moisture
Use different kind of bean You may use robusta, it naturally has more "caffeine" compared to Arabica, therefore can "hit" you harder
Use different kind of roasting profile the darker the roast, the bitter it is, but it has less caffeine.
- Pre-warming the equipment or insulating it basically the hotter the temperature you get bitter flavor, to avoid the "upleasant bitter" you may adjust the water temperature according to your preferences. Temperature loss often occurs as a result of heat absorption by the equipment itself (and therefore stale flavor), so pre-heat the equipment would prevent it
- Use finer grind Coarser grind can make your coffee under extracted
- Adjust the amount of your coffee
- Adjust the steeping time
In the end it comes down to your preference(s). No single technique is right for everyone. Enjoy your coffee immediately after brewing
My explanation might not answer your question directly, double filter affect your coffee, yes it is. But other factors simply can be neglected