Wizard’s Spell Mastery & Arcane Ward Synergy?

At 18th Level, Wizards of all Schools gain the “Spell Mastery” feature:

At 18th level, you have achieved such mastery over certain Spells that you can cast them at will. Choose a 1st-level wizard spell and a 2nd-level wizard spell that are in your Spellbook. You can cast those Spells at their lowest level without expending a spell slot when you have them prepared.

Meanwhile, at 2nd level, an Abjuration Wizard gains the “Arcane Ward” feature:

When you cast an abjuration spell of 1st level or higher, you can simultaneously use a strand of the spell’s magic to create a magical ward on yourself that lasts until you finish a long rest. The ward has hit points equal to twice your w izard level + your Intelligence modifier. Whenever you take damage, the ward takes the damage instead. If this damage reduces the ward to 0 hit points, you take any remaining damage. While the ward has 0 hit points, it can’t absorb damage, but its magic remains. Whenever you cast an abjuration spell of 1st level or higher, the ward regains a number of hit points equal to twice the level of the spell.

Provided a player character picked the Wizard as his class and the Abjuration School of Magic: If he was to select Shield (1st-level abjuration) as the 1st-level spell for his Spell Mastery feature, could that Wizard in theory recharge the ward with 2HP/Turn for free, all day? Also, would this imply that, provided he had the time between fights (At most 2.3 minutes, 23 rounds with Lv20 and +5 INT) he could heal the ward up to full by casting shield at the start of every round out of combat?