No, he only had Eve, after the timeframe when all the animals were brought before him. None of which were suitable for him. So how long did that take?
http://biblehub.com/genesis/2-20.htm
"And Adam gave names to all cattle, and to the fowl of the air, and to every beast of the field; but for Adam there was not found an help meet for him."
21 "And the LORD God caused a deep sleep to fall upon Adam, and he slept: and he took one of his ribs, and closed up the flesh instead thereof;"
22 "Then the LORD God made a woman from the rib he had taken out of the man, and he brought her to the man."
So how long does it take for everything to be brought before him to be named? Why would Adam realize none were suitable for him if not observing them mate, give birth, live out their lives and die?
I simply believe it was because years passed, naming those animals. And when a mate for him was finally created, he chose to die with her instead of loose her and be alone again.
Not that I believe it was a rib, but half of the genome. Hence when they mate the "two" recombine and "one" flesh is made.