In short: No.
Although of course, for "can" in its literal meaning, it's "yes".
First, hotels and the like are presently not allowed to accept you, as are camping sites, so you would necessarily have to do the equivalent of "wild camping". Which is your initial premise, too, if I understood right.
Also, and more importantly, doing a tour across the country (moving through large areas, and across regions needlessly, having contact with many people in many different regions) is exactly the thing that the government presently doesn't allow for. And seeing how traffic is greatly reduced to almost zero, you are likely (guaranteed?) to be noticed.
Even if bike tours across the country are not explicitly declared being illegal (neither is it explicitly illegal to, I dunno, spit at someone?), it's pretty darn obvious that you will be willfully acting against the Kontaktverbot in a very explicit and significant way, so you will not be able to talk yourself out of that.
This may have some very noticeable consequences from monetary fees in the hundreds to low thousands (depending on where you're caught) to possibly something more serious (not sure if "bodily harm" could be alleged, but might as well, especially in a few days from now, I wouldn't risk it).
As for wild camping (neglecting the other aspect), while some people -- campers -- argue that wild camping is not explicitly forbidden in Germany, and therefore allowed, that is far from the truth. The same people argue that it is explicitly allowed for everybody to go to "free areas" for recreational purposes. While this is true, it is only the half truth, though. To begin, "go" (as in walk) does not imply "camp", so that logic is flawed.
Further, it is explicitly forbidden to camp in many (in fact, most) places and under many conditions, nation-wide, state-wide, and regionally.
It is forbidden to camp in the forest (it is even explicitly forbidden to walk off the path after dusk, and sometimes even during the day) or in a variety of "bio areas" such as e.g. coasts, bioreserve, and bio-whatever-biotop-alikes, or near creeks (which, in summary, is almost everywhere, and it's very hard to tell where you actually may be allowed to camp).
It is explictly forbidden to do a hundred other seemingly harmless things that one also does while camping (anything that could possibly disturb an animal) during "vegetation period" which is from March to September, which is... right now.
It is further explicitly forbidden to do "wild camping" in Niedersachsen, Sachsen, Sachsen-Anhalt, Thüringen and Saarland, at all times, and without exception.
So, you may in principle only camp in some states, in no-forest areas, far from the coast and far from creeks, outside settlements, and whatnot. And... only if despite being "free area" it's not private property, which you cannot tell easily (camping on private property without the owner's consent is forbidden nation-wide).
That doesn't mean you couldn't do it and possibly get away with it. But I wouldn't deem it a very clever or risk-free endeavour right now.