Database backup size
Sql Server doesn't care 'where' your backups are ultimately stored.  Having said that, I can assure you that Sql Server 'knows' where the backups were 'created' (physical location) and stores that information in the MSDB database. Sql Server would try to use that information to generate a restore via SSMS GUI and the files wouldn't be there. Moving backup files around will also complicate an attempt to automate a restore plan by utilizing the information in the MSDB database tables because the files are in a different place than where they were originally created.  And, I think you definitely want an automated restore plan, especially with trying to restore a bunch of logs.  

In my opinion, the 'better' strategy is to allocate a separate disk drive or share with enough space to hold your intended backups.  I personally don't like maintenance plans for backups because they don't give you enough options.  A better choice is to use Ola Hallengren's maintenance scripts (backup, being one) - https://ola.hallengren.com/sql-server-backup.html