No. The problem is that Scripture does not present God's command to Adam not to eat of the fruit to be within what Scripture defines as a "covenant". You yourself pointed this out when you mentioned God's covenant with Abraham and walking through the cut pieces of animals. Scripture uses the term "covenant" in a very specific way. You are cheapening the meaning.
It does not matter how
@Martin Marprelate explains why he believes this was a covenant. The fact remains Scripture itself does not present it as a covenant so we have to look at the reasons for and against assuming it is. It may be a covenant. But it may also be only a command. Scripture itself presents God's statement to Adam only as a command (so we know we are safe there).
Why view it is a covenant?
God said to Adam that on the day he eats of the fruit death will be certain. Therefore should Adam not eat of the fruit he would live forever. This is the mentality but it is a formal logical fallacy. You are not only basing your conclusion on logic (which is fine) but on a logical fallacy (which is not fine). There are so many variables that you do not know that it is irresponsible to go beyond Scripture simply because
@Martin Marprelate says so (which was your "proof"). For all you know, if Adam had not eaten of the fruit he would have beat his wife for nagging him about not eating of the fruit (I know this is silly, but it is a serious point). God could have given another command that Adam disobeyed. A covenant lasts until a party dies (Hebrews 9). If this was a covenant then had Adam not eaten of the fruit Adam would have been free to disobey any other commands of God without the possibility of death (Adam could have not populated the earth, not subdued the earth, etc.).
You downgrade Scripture when you elevate these theories to the level of Scripture. That is my complaint. Not that you are wrong (I believe you are wrong) but that you are comfortable saying these theories are actually Scripture.