No. The LinkedIn Premium connection request limit is the same invitation limit a free account has. LinkedIn's help page on invitation restrictions puts Basic and Premium members under it alike, publishes no number for either, and says you cannot buy or acquire more invitations "while you've been restricted, or otherwise." The planner above opens with Premium picked, so you can see what does change.
What a paid plan changes instead
Paid plans change what goes with a request, and what you can do instead of one:
Notes. Premium members can add a note to every request. LinkedIn's page on personalized invitations adds that connection request limits may still apply. A free account gets only a few notes a month.
InMail. Each paid plan has monthly InMail credits, a separate budget from invitations. Sales Navigator has its own credits, and Premium credits cannot be spent there.
Searches. Premium Business, Sales Navigator, and Recruiter Lite raise the monthly limit a free account has on profile searches.
None of them adds connection requests.
How to read the planner
Switch the plan between free and Premium and watch the invitation figure stay put. The plan line in the breakdown changes nothing and gives the reason: LinkedIn applies invitation limits to every plan. The notes and InMail lines do change, each with the LinkedIn page it rests on.
The answers that move the invitation figure are about the account itself: its age, its network, and any recent notice from LinkedIn.
What to do at the limit
The same thing a free account does. Stop sending, wait for the restriction to lift on its own, and send fewer than before when you start again. Buying Premium in the middle of a restriction gets you notes and InMail credits, not your invitations back.
In Oneprofile, an InMail step spends your own LinkedIn InMail credits, and connection requests keep the daily and weekly limits you set on every plan.