No. Your Instagram account needs to be public for Growth Viral to work.
Here’s why: when we engage with someone, they check out your profile and decide on the spot whether to follow. A public account means they can see your content straight away. A private one gives them nothing to look at, and most people won’t go out of their way to request access to an account they’ve only just come across.
Switch to public before you get started. If you go private partway through, expect your results to drop off noticeably while it stays that way.