Simple answer: in our universe, definitely no.
You're hitting here on an idea known as Loschmidt's Paradox: given that microscopic laws are time reversible, entropy should have the same tendency to increase whether we run a system forwards or backwards in time, exactly as you understand.
The fact that this understanding is manifestly against experimental observation can be explained if we observe that the universe began (i.e. found itself at the time of the big bang) in an exquisitely low entropy state, so that almost any random walk in the universe's state space tends to increase entropy. Likewise, in the everyday world, things "happen" when a systems are not in its maximum entropy state: they spontaneously wander towards these maximum entropy states, thus changing their states and undergoing observable changes. Sir Roger Penrose calls this notion the "Thermodynamic Legacy" of the big bang and you could read the chapter entitled "The Big Bang and its Thermodynamic Legacy" in his "Road to Reality". In summary, we have a second law of thermodynamics simply by dint of the exquisitely low entropy state of the early universe.
 Loschmidt's own name for it is "reversal objection" (umkehreinwand), not "paradox". Paradoxes, i.e.
genuine logical contradictions cannot arise in physics, otherwise they could not be experimentally observed.