Yes, you lose 10 points for each card in your hand beyond the 7th card, regardless of whether any of your cards have negative end-game point values.

This is supported by the following rule:

• "Excess cards: For each card in your hand beyond the 7th card, lose 10 points. At this time you’ve already accounted for other points from these cards—those points are still valid. This penalty represents the unwieldiness of managing a larger house and encourages players to focus on cards that work well together, not simply more cards."
  (Page 7)

This means:

• You first total all points (positive or negative) from your cards' core values and end-game bonuses.
• Then, for each card over 7, you subtract 10 points, regardless of the cards' other point values.

Example:
If you have 9 cards, you lose 20 points (10 for the 8th card, 10 for the 9th card), even if some of those cards have negative end-game points.

Source: page 7.

Source: Core Rulebook (pp. 4, 6, 7)