In place upgrade from Express 2005 SP 4 to Express 2014, does database size limitation follow? We are currently attempting get around a file size limitation issue with our database. The database file size hovers around the 4GB mark (the database size limit is 4GB in SQL Express 2005). We always trim data past a certain age to keep it below this limit. 

To avoid this, we are looking to perform an in place upgrade to SQL Express 2014 (10GB size limitation). Will the file size limitation follow the database when utilizing the in place upgrade?
No it will not follow, you will be able to utilize the migrated database up until the 10GB limit. 

I've written an article on maximizing space savings with regard to SQL Server Express, which may also be of interest to you to help reduce the your periodic data pruning further. 

You may also want to consider upgrading again after 2014 to 2017 or 2019 to keep up with the latest advances in SQL Server features, stability, etc.