Yes, power cards can be bought after a monster has reached 20 victory points but before the end of the turn.

This is supported by the following rules:

• The game ends "at the end of a turn when a Monster reaches 20 or if only one Monster remains" (page 6).

• The turn sequence is:

  1. Roll Dice
  2. Resolve Dice
  3. Enter Tokyo
  4. Buy Power Cards
  5. End of Turn
     (page 4)

• The rulebook specifies: "If you reach 20 and reach 0 in the same turn because of a Power card, you are eliminated. You must survive your turn to win." (page 6)

This means:

• Reaching 20 victory points does not immediately end the game; the turn must finish.
• The "Buy Power Cards" step occurs before the "End of Turn" step.
• Therefore, after reaching 20 victory points (for example, during the "Resolve Dice" step), you still proceed to the "Buy Power Cards" step and may purchase power cards before the turn ends and the win is checked.

Source: pages 4 and 6.

Source: Core Rulebook (pp. 2, 3, 4, 5, 6)