Yes...provided the plants are sufficient in number for the fish load.
Plants need nitrogen as a major macro-nutrient. In the aquarium, nitrogen occurs as ammonia/ammonium, nitrite and nitrate. Plants have a substantial preference for nitrogen in the form of ammonium.
Fish and other biological processes create ammonia which is highly toxic to plants and fish at quite low levels. In acidic water the ammonia changes to ammonium which is basically harmless to fish and plants. Ammonia de-toxifiers (as in Prime) usually detoxify ammonia by changing it to ammonium. Plants in the aquarium use the ammonium as their nitrogen, and they use a lot of it. In basic/alkaline water, plants use two methods of using ammonia, and one involves converting it in the cells into ammonium.
They are so good at doing this they out-compete the nitrosomonas bacteria. This is why in a well-planted aquarium the nitrification bacteria will be fewer in number than otherwise; the plants consume most of the ammonia/ammonium. That is why there is a low level of nitrate in a planted tank; the ammonia used by nitrosomonas bacteria to produce nitrite which is then used by nitrospira bacteria to produce nitrate is minimal. A high nitrate reading in a planted tank means either there is far too much biological nitrification occurring, or something has upset the natural biological balance.
So, if you plant an aquarium well at the beginning, you can add fish to the aquarium at the same time. Provided you do not overload the fish with too few plants, there will be no "cycle" occurring that will be detectable. Some ammonia will be used by nitrosomonas bacteria, but it will be so minimal the bacteria will easily establish themselves and no harm will occur to the fish from ammonia (or nitrite).
The number and type of plants you list will be quite adequate in a 75g aquarium to handle the lone SD [all right, I won't say anything about this as you've asked
] and a couple dozen small fish. Corydoras often do not fare well in new tanks, but that is largely due to the ammonia which they cannot tolerate. Corydoras travel badly, simply because of the high ammonia in their shipping containers. But in a well-planted tank, that is not going to be a problem. And using the filter media to seed the new tank is an insurance policy of sorts, and certainly won't hurt anything.
Last July I moved my tanks and re-set the 115g, 90g and 70g with tap-water washed or dry gravel, new unused filter media, and moved all the plants and fish in one day with no losses, no stress and zero ammonia and nitrite readings from day one. If you still are skeptical
, I can give you links to articles by microbiologists and such.