absolutely it could have, but the cost of doing business through spring training was a very small part of the calculation. It was 99.99999999999999% leverage based decision making for CBA negotiation. A few million per team on flights and coordination of ST is very small, compared to a bad CBA that takes effect for 5-10 years that can be hundreds of thousands to millions per player per year. if half your roster is effected by ML minimum, 20 roster spots * 300k*30 teams * 5 years is $900 million. There's alot at stake.
Having a promise in good faith not to strike/lockout is a CBA, Collective Bargaining Agreement.
I for one feel that the players would have chosen to start the season, and start the strike somewhere just before the all-star break to really put pressure on the owners to get the season restarted to stop the bleeding on lost All-Star revenue and the longer it goes on, the more likely it impacts post season revenue, to really pressure the owners to cave.
The owners, under the same assumptions locked-out the players as early as possible, this takes away the player's leverage, and gives a relatively long deadline where they can be patient and let the players come to them. Now the players would try to be patient as well... the longer it takes the higher the likelihood it eats into the owners checkbook
My guess is there won't be any movement until February at the earliest