It is possible but the question I ask my clients is why? I've found there is nothing you can't do in Portal development that you can do in ASPX development, its simply taking the time to learn how to do it and do it right. For instance if you have custom membership or authentication, most new Kentico developers would simply go for the ASPX development model because its familiar to them. Bad part is this becomes a maintenance nightmare.

If you take the time to learn the system or hire a freelanceer/contractor (like myself) to do the work and/or teach you how to work within Kentico then you will be miles ahead of most others.

I'm guessing since you only have a base license your site is fairly simple? What can you tell me about the site or what makes it special where you might or would need to use ASPX development model?