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Out of the box, not reliably.
If you're doing explicit campaign tagging, you can have five hidden fields on your forms, each capturing a UTM parameter. Minimum viable product is to have them caught from the URL string, and then better version is URL string->cookie->hidden fields. Then you'll have the UTM parameters (including utm_term, which is the keyword) on the lead record.
Auto-tagging AdWords links won't be written to hidden fields this way, though, because the auto-tagged links from Google don't follow traditional utm parameter strings.
For optimization purposes, I usually do keyword-level analytics reporting through Google Analytics and the goals you already have set up—for conversion-rate-optimization, that's mostly all you need. That's assuming your business has longer sales cycles and fewer numbers of customers. By the time I find out that "mananaging company debt transactions" led to one closed-won lead, it's mostly not actionable, especially since keywords are going to be long-tail for the most part when you're doing broad-match PPC keywords.