It is possible!
In any case this is the list of items I was able to confirm could be received by the game.
Mixed Syrup
Maple Syrup
Earring of Magnetism (Start Battle with a Power up)
Umai-bo Snack 1, 5, 6
Hard Knuckles (Atk 58, Int 10)
One Two Puncher Atk (280 Atk!!!!)
Faerie Elixir
Sinclair (Atk 100)
Tenper Tablet (Stones enemies on Atk but loses control)
Star Earring (Motor Mouth level 3)
Oil of Paralysis (chance of paralyzing one enemy)
Shock Oil (stuns a single enemy)
Robot Puncher (Atk 125)
Paralysis cure
Lavender
Walloon Sword (240 Atk!!!!)
Immunity Pill (Care Tablet)
Hazardous Heal (Heals 30% in exhange for a status ailment)
Iron Helmet (Def 25)
Lady Fingers
Medical Rinse (3% Regen)
Meat
Lavish Idol (Int 1)
Booster Clip (Atk 125)
Resurrection Mist
Refreshing Syrup
FanFics (X, ?!, …, O)
Ring Mail (Def 20)
Victory Card (All Allies Guts +50%)
Baselard (Atk 180, Ashton)
Wooden Shield
Succubus Perfume
Gold Idol (Hit 1)
Padded Armor
Weighty Ring (Crt 3 , Guts 6, Weak to Wind)
Ring of Resistance (Reduces spell damage by 90%, 10% chance it may break)
Veil Piercer!!! (480 ATK!!!!!!!)
Vegetables
Fire Puncher (699 ATK, Precis)
Bubble Lotion (Stones enemies on Atk)
Froghead (Def 1, Guts 5)
Stone Cure
Flame Sword (160 Atk, hit 20, Crt 10, Fire Elemental)
Super Charger (Atk 650, Precis)
Knights Shield (Def 10, Avd 60)
Seafood
Potion of Might Atk + 30%
Smoke Mist (chance to decrease movement speed)
Boots
Dull Blade
Wolfsbane
Mental Potion (Int +40%)
Robe
Taloned Knuckles (Atk 165, not Renas)
SORCERESS KNUCKLES!!!!! (1000 ATK!!!!, 180 INT!!!!)
Fine Shield (Def 15, Avd 70)
Experience card (Double EXP)
Pixie Perfume (Int +50% , makes one ally impossible to control)
Defense Bomb (DMG done to enemies in relation to their defense stat)
Encyclopedia (Atk 500, Int 100)
Atomic Puncher (Atk 1120, Hit 55 Precis 55
Theory of Symbology (Atk 290, Int 100)
Creaky Rod
Marionette (Revive 10% Atk 50%)
Suede Boots Def 5
Steel Armor
Sword of Marvels
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