Yes. On a Texas school construction job let as competitive sealed proposals, the district ranks offerors on the published criteria and can award to someone who is not the low price.
Facility construction, rehabilitation, alteration, or repair for a Texas school district runs under Texas Government Code Chapter 2269, not under the Education Code purchase methods that cover goods and non-construction services. Education Code 44.031 sends construction delivery to Chapter 2269. Competitive sealed proposals are Subchapter D, starting at 2269.151: the district requests proposals, ranks the offerors, negotiates as the statute lays out, then contracts with a general contractor.
Under 2269.154 the district opens proposals publicly, reads the names and any monetary proposals aloud, then evaluates and ranks every proposal against the published selection criteria within 45 days of opening. Under 2269.155 it selects the offeror that offers the best value based on those published criteria and the ranking, then first tries to negotiate a contract with that selected offeror. The district and its architect or engineer may discuss scope or time changes and any related price change. If that negotiation fails, the district ends it formally in writing and moves to the next ranked offeror until a contract is reached or every proposal is rejected.
For the boiler packet, write to the scoring sheet line by line. Put school HVAC jobs first under past experience, with campus type and when you finished. Tie the schedule to the school calendar and any occupied-building constraints the packet names. For safety, describe the program you actually run on jobs like this and answer whatever record the form asks for. Price still matters, but under 2269.155 it is one published factor among the rest, not an automatic winner.