When a Builder changes a Dispatch Platform into a Siege Tower, does it get its starting upgrades?

No. You ignore the Siege Tower's shown starting upgrades, and maintain the same upgrades it had before the Builder talent was used. For example, a Dispatch Platform spire was constructed during the build phase, with its starting upgrades of 1 attack and 1 range. During the onslaught phase, the Brawnen use a limited build option to add a fortification upgrade to it. Later, the Brawnen use an Architect's Builder talent to promote the Dispatch Platform into a Siege Tower. The Architect can do so even if the Brawnen do not have the Smelter Level 1 advancement. The Dispatch Platform chip is flipped over. This spire no longer has Splash but now has Raze, and has an upgrade capacity of 4 instead of 3. Its upgrades do not change; it maintains its upgrades of 1 attack, 1 range, and 1 fortification.