Can you do it - yes you can, should you do it, probably not.
A restore would potentially require the full backup and EVERY differential backup since (300+), so if you lost one of the incremental backups you could be in trouble.
Using a cumulative incremental (instead of differential incrmental) would be a slightly better option, as then you would only require the full backup and the last incremental backup - however over time the cumulative incremental would become quite large.
As always the best option is to perform regular full backups to improve your recovery options.
As per @davidmoline 's post - this is not a good idea.
Your customer needs to look at total amount of storage on clients that need to be backed up, document retention requirements, and the purchase sufficient storage (disk, dedupe disk or tape) that will allow regular full backups (at least once a month, or even better - weekly Full backups).