Is it possible to use the assets modal on the front end?
Craft supports all of the fields within the Control Panel, but not on the front-end – the number of scenarios they would need to support on the front-end increases the scope of supporting a field dramatically.

Craft does however support submitting Assets from the front-end (an example with Guest Entries) and restricting Assets to user specific folders using Dynamic Subfolder Paths.  

So you can do what you are describing, and may even be able to reuse some of the code they use to build out the functionality, but (currently) you will have to adapt it to your scenario and maintain it yourself.