Hi @Shaadi_Mehr
There isn’t a hard limit (I am double checking this for ORG) and the Upload tool has a resume function.
Guide → Getting Data into Galaxy
The guide covers advanced loading from the command-line, too. Useful for batch work, very large files and automation from an API script.
That said, you might run into practical limits if 15-20 people are all attempting to load larger data from their desktop up to any remote site, all using the same internet connection. This isn’t a Galaxy constraint and is more about the throughput in the connection itself.
As a workaround for connections with slower “up” speeds, you could consider having just a few people load the data, then they could share the history, and others could import it? Or, you could put the data up into the cloud somewhere and allow people to load it by URL? That would remove your local connection speed from being a factor.
I’m mentioning the share ability since is a big part of why Galaxy can be so helpful, and it is a topic we always cover in training. Useful for collaboration, when getting help, and later on when publishing work. 
If you share what kind of data this is and how large, I might be able to share more specifics.