Spanxxx is right. Also, if you have a basic set of classes for both your sql and common functions, you will develop even faster.
For example, where I work, after a year of work, we developed a good set of classes and a common way to access data. Each table in the db has its own class with add/update/delete/get single/get collection. Those classes use a common db class which then can use MSSQL or MySQL (this part still needs alot of work) to connect to the db and perform the query. We then wrote a program to read the fields from the table and generate our class and stored procedures (we mainly use MSSQL). Basicly, we develop the database and then generate all the classes off it. Sure, alot of custom methods have to be written, but the majority of the grunt work is done. Most of our software has some sort of data processing app. For this reason, all these classes are compiled into a dll that both the website and the applications use. What took us 2 weeks before we got this process developed only takes 2 days now.
Another class is common web functions. Set default selected in a listbox/checkbox/combo box, etc. Another class is common things for reporting, such as GetFirstDayOfMonth (passing in a DateTime.Now), LastDayOfMonth, etc. All this stuff seems simple and "well, I can just do it each time I need it", but having it all common and prebuilt is nice!
I would never go back to ASP unless I was going to get paid alot more and even then, I'd try to convince them (client/boss) to go .NET.
Edit: To actually answer your question (went of in a different direction
), yes, you can use traditional asp in an asp.net project. Make an asp.net project, place all your asp files in it, and slowly convert if you can't do a 100% convert right away.