Is it appropriate to send a LinkedIn request to the recruiter after not being offered the job, due to the hiring budget being lower than my salary expectations?

I applied for a job with a company I'm very interested in and passed the first screening interview. Unfortunately, the manager for this position said I was a bit too expensive, and they realized they probably needed to lower their qualifications for this role. I wasn't too surprised since my initial reaction to seeing the job description was that the responsibilities vs. qualifications didn't quite line up. However, the recruiter was keen on keeping in touch just in case a role opened up that would be a better fit. I thanked her and said I'd love to keep in touch and am very interested in working for the company in the future.

This happened about 3 weeks ago. Would it be appropriate to send a connection request via Linkedin? I know that recruiters are swamped with applicants so I just don't want to fall off her radar. Of course I'll also be proactive in checking their job opportunities every so often, but I do want to express my genuine interest in keeping in contact with the company.

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