So I have been trying an experiment. You try it. I haven't sent an inmail in 2 months. I have only sent invitations to connect with a brief explanation of why. It seems to be working well. It could possibly be working better. Maybe it is more personal? I don't know. I wanted to see if anyone else had tried this. Someone with not much $$ to spend on LI Recruiter- this could be your answer.
Thanks! Your contacts - the ones that are not connections, but are saved while browsing or imported - are visible only to you. There's no need to worry that "your contacts" will be notified in any fashion or invited without your knowledge.
You can see the "contacts" as your own database of profiles.
That said, if you "save" a profile (any profile) of a person on LinkedIn to your contacts by pressing that "star" icon, then connecting with them is easier; there will be a link provided for that in the contacts. You are free to use or not to use it.
... but I don't mean to say it's not worth paying. I have Talent Finder and we also have LIR (Recruiter).
With TF, it's a matter of convenience, not only in profiles' visibility but overall. I also like my InMails.
I can't be sure and please don't hold me responsible, but this link may offer you one month free trial. of the "executive" account. You need to be logged in. Don't forget to cancel if you are not buying.