Would smoking or applying a nicotine patch, by introducing additional nicotine, which also binds to the acetylcholine receptors to some extend counterbalance the effect of atropine?
Disclaimer: I do not work with receptor bindings very often.
First point binding sites... Both Atropine and Nicotine bind to Cholinergic receptors. However receptor binding is not competitive as the rector sites for each neurotransmitter is different (NT): Atropine is a direct-antagonist of Muscarine binding with AChRm (muscarinic receptors) while nicotine is a direct agonist of AchRn (nicotinic receptors).
Atropine however does inhibit the action of nicotine in mediating ion currents on cholinergic receptors in the Central Nervous System (CNS). However this depends on the concentration of each NT in the neural system, low does of Atropine are enough to block high concentrations nicotine. So while a high concentration nicotine, say from an e-lite might be enough to save your life from Belladonna poisoning, I wouldn't personally go out of my way to test the theory! However the Nicotine from a cigarette probably wouldn't be a high enough dose to counter 1um of atropine. However say you did drink some belladonna because you have evil 'friends', but then you smoked a cigarette with enough nicotine to save your life. You then encounter another problem...half-life. The half-life of atropine is 2 hours, the half-life of nicotine is 1-2 hours! Do you want to risk that last hour if it takes two hours to see a medic or if you are transported back in time to medieval england!? Incidentally if you were poisoned with belladonna being transported back to medieval England would make sense. Your only option at this point, after the first hour, is to keep smoking (nicotine metabolites have 20 hour half-life, but there action is reduced), this is one of only a few situations that smoking may prolong your life! Although you will need some pretty potent tobacco to achieve this, better make sure you land in Tudor England instead.
Moral of the story...don't time travel! I'm looking at you 'doctor' with the blue box.
If you do believe you are in medieval England or the Roman empire please ask someone to call a Neurologist or a psychiatrist! If they say "what's a neurologist/psychiatrist?" you are completely sane, congratulations you have achieved time-travel.
Specifically information about competition between atropine and nicotine concentrations...
"At the holding potential of 80 mV, 1 mM atropine inhibits 1 mM acetylcholine- induced inward currents mediated by rat a2b2, a2b4, a3b2, a3b4, a4b2, a4b4, and a7 nicotinic receptors by 12–56%. Inward currents induced with a low agonist concentration are equally inhibited (a3b2, a3b4), less inhibited (a2b4, a7), or potentiated (a4b2, a4b4) by 1 mM atropine. Effects on the more sensitive 44 nicotinic receptors were investigated in detail by systematic variation of acetylcholine and atropine concentra- tions and of membrane potential. At high agonist concentration, atropine inhibits 44 nicotinic receptor-mediated ion current in a noncompetitive, voltage-dependent way with IC50 values of 655nM at80mVandof4.5M at 40mV. At low agonist concentration, 1 M atropine potentiates 44 nicotinic recep- tor-mediated ion current. This potentiating effect is surmounted by high concentrations of acetylcholine, indicating a competitive interaction of atropine with the nicotinic receptor, and potentiation is also reversed at high atropine concentrations...The apparent affinity of atropine for the agonist recognition sites of the a4b4 nicotinic acetylcholine receptor is estimated to be 29.9 mM." Zwart and Vijverberg (1997)