Would it be appropriate to contact a job recruiter on linkedin?

I found a job out of state on indeed dot com. I was able to provide my information and upload a resume that will be sent to the prospective employer. Amazingly in the job description it listed the HR persons name and said to contact them, however there was no number provided.
I Googled the HR person and found them on linkedin. I have a profile on linkedin that lists my job history, experience and certifications along with other vital information.
Would it be appropriate to contact her through linkedin and if so what should I say?
Maybe "Hello (insert her name) I applied for the (insert job name) position with your company and feel I would be a great match for this position. Please feel free to contact my references and you may contact me at (insert my #)"
Any ideas folks?