To answer your specfic question, no it won't slip or burn up just because it doesn't have high performance parts in it.
Since you are concerned about budget, just run it and spend the money on the recommended converter.
What's a "mild" shift kit? (This will make a pretty big difference)
If it's not at least a TF2 or equivelent, then have them do that and let it go.
That and an external cooler should get you through multiple racing seasons.
JMO
