Does Quickdraw bypass equip costs?

Yes, Quick-Draw bypasses the Equip cost when you play the equipment from your hand.

According to the rules and FAQs regarding the Quick-Draw keyword:

• Rule 745.1.d: Quick-Draw is functionally short for “[Reaction]” and “When you play this, attach it to a Unit you control.”
• How it works: When you play a piece of Gear with Quick-Draw from your hand, you pay the Energy and Power costs printed in the top-left corner of the card. Because of the Quick-Draw ability, the gear automatically attaches to a unit you control as part of the play process. You do not pay the Equip cost (the cost listed in the card's text box) for this initial attachment.

Important Nuances:

• Subsequent Attachments: If the gear becomes unattached later (e.g., its unit leaves the board) and you wish to attach it to a unit again, you must use the standard Equip activated ability, which does require paying the Equip cost.
• Mandatory Attachment: If you have a legal target on the board when you play a Quick-Draw gear, you must attach it. You cannot choose to leave it unattached.
• Play Costs: You must still pay the Energy and Power costs (top-left corner) to play the card. Quick-Draw only bypasses the Equip cost.