By Google Alert I assume you mean
these guys? I don't know anything about them or how they do their service, but there is a free service at
DigitalPoint that uses Google's API. This tool operates within Google's terms of service so it is unlikely it will have any effect on your site at all.
That said, it is unlikely that the tool you are using would have any negative effect on your site. There is another thread about how much Google knows about webmasters, but I think they know somewhat less than what is suggested in that thread. I doubt they know you are using that service and what site is yours; even if they did, it would be too easy to hurt a competitor if Google used that knowledge to "punish" your site in the SERPs.