Aye, you will. By the text you yourself quoted, Kensai still suffers spell failure chance. Proficiency with armor does not negate spell failure chance, nor does it reduce it, proficiency only affects Armor Check Penalty. Same as if you were to take the Armor Proficiency feats.
From the feats page on paizo.com:
Armor Proficiency, Light (Combat)
You are skilled at wearing light armor.
Benefit: When you wear a type of armor with which you are proficient, the armor check penalty for that armor applies only to Dexterity- and Strength-based skill checks.
Normal: A character who is wearing armor with which he is not proficient applies its armor check penalty to attack rolls and to all skill checks that involve moving.
Special: All characters except monks, sorcerers, and wizards automatically have Light Armor Proficiency as a bonus feat. They need not select it.
From the armor page on paizo.com:
Armor Check Penalty: Any armor heavier than leather, as well as any shield, applies an armor check penalty to all Dexterity- and Strength-based skill checks. A character's encumbrance may also incur an armor check penalty.
Shields: If a character is wearing armor and using a shield, both armor check penalties apply.
Nonproficient with Armor Worn: A character who wears armor and/or uses a shield with which he is not proficient takes the armor's (and/or shield's) armor check penalty on attack rolls as well as on all dexterity- and strength-based ability and skill checks. the penalty for nonproficiency with armor stacks with the penalty for shields.
Arcane Spell Failure Chance: Armor interferes with the gestures that a spellcaster must make to cast an arcane spell that has a somatic component. Arcane spellcasters face the possibility of arcane spell failure if they're wearing armor. Bards, magi, and summoners have class features which allow them to wear certain armors or even shields without incurring any arcane spell failure chance for casting spells from their class spell list.
Casting an Arcane Spell in Armor: A character who casts an arcane spell while wearing armor must usually make an arcane spell failure check. The number in the arcane spell failure chance column in the Armor and Shields table is the percentage chance that the spell fails and is ruined. if the spell lacks a somatic component, however, it can be cast with no chance of arcane spell failure.
Shields: If a character is wearing armor and using a shield, add the two arcane spell failure chances together to get a single arcane spell failure chance.
Quoted from the Kensai archetype on paizo.com
Weapon and Armor Proficiency: A kensai is proficient in simple weapons and in a single martial or exotic melee weapon of his choice. A kensai is not proficient with armor or shields and suffers normal arcane spell failure chance when casting magus spells while armored.
Iaijutsu (Ex): At 7th level, a kensai applies his Intelligence modifier as well as his Dexterity modifier on initiative rolls (minimum 0). A kensai may make attacks of opportunity when flat-footed, and may draw his favored weapon as a free action as part of taking an attack of opportunity. This ability replaces the medium armor ability.
Iaijutsu Focus (Ex): At 13th level, a kensai may always act and may draw his weapon as a swift action during a surprise round, though he is considered flat-footed until he acts. During a surprise round or when attacking a flat-footed opponent, he adds his Intelligence modifier on damage with his chosen weapon (minimum 0). This ability replaces heavy armor.