>>722991091
She has ~1/14 chance (not counting the chance to give stats) to give you groundwork.
Base chance of a "!" to appear on each training is 10%. Gold Ship has 40% Hint Frequency.

So the actual chance for her to give you groundwork for each training is
1/14 * 10% * 140% = 1%, equal to the base chance of inheriting a groundwork from 1* groundwork spark without counting the affinity.

You train for maximum 75 turns, multiply that with 1% then your expected value is 0.75 still below 1.

TLDR you better sacrifice a slot for Guts Air Groove.