If you've used sterilized potting soil, which all plants in pots deserve my opinion of course, you bet you can. If you are using garden soil in your pots it would be best to not reuse. Never allow your plants and their pot to sit in the puddle of water in the saucer. I've seen and understand nurseries that during incredibly hot weather sit their pots in water. But that is the only instance. In fact you should raise the bottom of the pot about a 1/4' from the surface of the saucer or any surface the pot drains upon. Use tiles, flat rocks even specially made 'pot feet' some that are made to look like tiger paws, or frog feet. That really improves drainage.
The soil that comes out tells me you've newly transplanted your plants into new pots and hopefully sterilized potting soil. That stops very soon. I've told people to use old nylons or chunks of old nylons you know for women's legs? to cover the drainage hole. That works well to keep soil in its place. Don't use rocks or gravel or pieces of clay pots or packaging peanuts above the drainage hole as that creates a perched water table and causes very bad drainage. Another discussion.
If you are not using sterilized potting soil just dump that stuff in your sink or out of doors. Plants in pots are totally dependent on their human stewards. Give them the best soils, as much light as possible (careful with this as plants used to low light have thin epidermis that won't protect them from sunburn), fertilizer in the correct amounts/formulations and drainage. Plants are tough and sure they will live but they won't be healthy and vigorous.
Do you have water restrictions? I also never use tap water for my indoor or outdoor plants. Of course I have well water. But indoor plants should have distilled water you purchase. Otherwise, the salts in the water will cause burned tips and margins. Filtered tap water would be great.
I wouldn't bother saving the 'saucer' water to use for my other plants. What are you doing for fertilizer? If you use water from fertilized potted plants that water will have fertilizer chemicals and just a wee bit too much fertilizer will kill plants sure and certain.