The quality of performance on your computer doesn't (or shouldn't) affect the resulting quality after a conversion. In PowerDirector, there is a Speed-Quality slider bar for the user to decide. If this converting mechanism exists, my advice is to keep it at the highest quality, despite the performance. The only factor that should vary, based on the PC's performance, is the rendering time it takes.
You should also realize that converting AVCHD to AVI, you will have the limitations (types of information loss) of both formats. AVI compresses in a different way than does AVCHD. AVI results in the lesser amount of information loss, but the type of loss is different. The results may not be noticeable, so your best bet might be converting to AVI as you mentioned above.
If Adobe Premiere edits AVCHD smoothly enough, I would work with the AVCHD content as it is.