I'm going to say no, this is not a viable method of crop rotation. I'm not going to rehearse @Willk's answer as it is good, but what I will point out is that there are a number of other factors;
Crop Timing II
It's not just that different crops will only grow at different times of the year, but certain crops also grow at different rates. Corn for instance will take (on average) around 80 days to grow, but potatoes will take around 120. This is assuming good soil with ideal conditions for each crop; your lack of fertilisers will alter that making the possible growth figure even more variable between crops.
Leaving a field fallow for 40 days may not be a bad idea, but it's still inefficient. You may want to find a crop that grows quickly in the interim that can plug this gap, but the timing of field based rotation is still more complicated than rotating through a single crop across all the available land.
Fruits & Nuts
These are 'asset' based crops; you have an asset (a vine or tree) that produces yields for several years in a row; that effectively blocks your rotation strategy or at least sections off part of the land so that its quarantined from conventional crop rotation. So long as you're fine with an orchard being exempt from rotation, no problem. That said, grape vines (for instance) are even less ephemeral than trees, so at least you'll always have wine.
A special case worth mentioning here is Sugar Cane. This is really a grass, but it has a 7 year cycle for the plant as it produces yields. Again, that effectively quarantines the land, although the simple solution here is to give up sugar, if you're prepared to do so. In some environments, it's a nice cash crop.
Because you don't have fertiliser, you're definitely going to want to plant beans or peas regularly in your rotation. Legumes are important because they're nitrogen fixing plants (they actually put nitrogen in the soil, rather than extract it). Most modern fertilisers are called NPK fertilisers (Nitrogen, Phosphorous, Potassium) so the added nitrogen will be useful to conventional rotation without fertilisers. Your best use of this would be to harvest the beans, then plough the plants into the soil to decay and release even more nutrients.
What this last point highlights is that rotation is only useful if you know what each crop adds to (and more importantly extracts from) the soil. This method of farming is useful on small scales because it means that you have a wider variety of crops maturing at the same time, but it's certainly less efficient and introduces other considerations like orcharding and viticulture that are going to break up the possibility of rotation.
In that sense, my no above is qualified by the idea that you're trying to produce on a large scale. If you're not, then it's a different story but in that case I'd start doing some research on Permaculture. This is an even smaller scale implementation of what you're describing in your post and may be a good place to start in terms of understanding the chemistry and biology involved in crop rotation and simultaneous planting strategies. On a small scale permaculture would give you more sustainability AND more variety in terms of sustaing (say) a family with limited land resources.