No it won't... The caret specifier for 0.0.x packages means "this version and this version exactly".
https://docs.npmjs.com/misc/semver#caret-ranges-123-025-004
And to be honest, it's news to me. Sorry i impulse downvoted you...
^1.2.3 := >=1.2.3 <2.0.0
^0.2.3 := >=0.2.3 <0.3.0
^0.0.3 := >=0.0.3 <0.0.4