IMO/E...no, especially during the cycling process with fish-you risk their health and well being.....Some of the staff at some pet shops often fail to give proper information, as well meaning as they are....
On a 10gal filtered tank without live plants and without testing products on hand-while establishing the nitrogen cycle-I would recommend at the very least 2 water changes a week for the first 6 weeks...1-50% water only and 1-50% with substrate vacuuming
The weekly 50% with vacuum will be for the life of the system to maintain water quality....
Then during the first 6 weeks unless you have test products on hand-for safety make a second 50% water only-
If you have test products on hand-base the 50% water only on test results of ammonia, nitrite 0.25ppm or greater
Once you have nitrate 5-10ppm without ammonia, nitrite spikes you are most likely cycled
Several things can change the cycling process-water temp, pH, live plants, stocking, additives to name a few....
The beneficial bacteria for the nitrogen cycle are sticky and adhere to all the surface areas within the tank, in the top layer of substrate and in the filter media-very little are in the water column and so water only changes will not stall or hurt the process-but over cleaning can.
The bacteria need surface area, food source and oxygen to colonize-the BB can suffocate by too much mulm/debris, be killed by chlorine/chloramines and if allowed to dry out or go without enough oxygen or limited food will start to die and/or consume each other -
Filter media needs a swish/rinse in the bucket of old tank water with a water change a couple of times a month to remove the big pieces of gunk-the filter media should look dirty....You don't need to change the filter media unless it is falling apart.
If the filter media is the combined type with sponge and carbon and if you plan to use carbon (not needed) this needs to be changes per package direction since it is limited and can't be recharged-
Use of carbon is more of a personal choice-water changes generally will do the same thing as carbon...If you do opt to use carbon and it is combined with the sponge-cut a piece of sponge off and add to the new media for a week or so to seed it...... with the bio-wheel as long as it is functioning properly this should house enough BB to prevent spikes-but you should always monitor the tank as a general rule and make water only changes as needed....
I seen in one post about you adding corydoras-for one they are not algae eaters and will do very little in the control, since they are schooling species they will do much better when kept in the proper numbers and you will get to enjoy their playful behaviors as well....
With any species of fish-when you fail to keep them properly and meet their needs you risk stress and this in turn can compromise immune response and you end up with sick fish...