I have a DNN application which is running on v3.2.2. We have decided to upgrade this application to v6.2 or higher. While researching online we came across suggestions to do iterative upgrade from 3.2.2 to 4.0.5 to XXX.. etc. 

We were thinking of a different approach but would like to know if anyone else has tried this earlier what was the result?

The approach we thought of is to take the v6.2.5 and then recreate the custom modules and also any changes related to the web part. We are thinking of manually executing all the upgrade SQL scripts on our v3.2.2 database so that we can make it in sync with v6.2 and also retain all our settings and other information. The reason for this is that we have more than 400 sites implemented.

Is this a viable approach? What are some of the challenges that we might come across?

Instead of upgrading step by step as mentioned in the link that you forwarded, we are planning to  directly install the 6.2.5 version. What i want to know is 

1. Is it possible to migrate all the data from existing database (v3.2.2) to the new database? I understand that there are schema changes between v3.2.2 and v6.2.5 and this may not be a solution. 

2. If option 1 is not possible could we execute all the SQLDataProvider scripts between v3.2.2 to v6.2.5 on the existing database to upgrade it to the latest? Would this approach work? We could point the application to this database which will already have all the sites implemented in it.

 neither is an option as during upgrades we apply database changes through scripts but also through API requests in our upgrade code (for when we need more granular checking/loops etc.). As such upgrades are only supported via the conventional method i.e. overwrite the current site with an upgrade package.