I have a minor league player I am looking at moving up but my concern is he has no power.

He has a great CF makeup

His batting ratings are such:
Batting eye - 87
vR- 65
Contact - 67
Power - 1, yes, one
His speed is 100 and his baserunning is 92, with an 89 bunt.

Will he be able to produce with the low power over time?

He will be a solid lead off batter capable of 100+ steals and 125+ runs in an alright lineup.  He might hit .270 and have an OBP around .350 depending on the park.  He'll have almost no extra base hits but he could lead the league in infield hits and most of his hits would turn into doubles and triples by way of theft. I love these types of players, I'd prefer to have one in every lineup with 80+ vR and contact though ;)
Oh and to answer your question...the importance all depends on the needs of your team...he holds value to a lineup...not to drive in runs but as a table setter and scorer, absolutely.

See Otis Nixon