UA's boarding is done via 2 lanes, a red carpet lane and an economy lane. The order is:

Red carpet boarding announced first for: Global Services, 1K, First/business class

Then economy lane boarding announced for Premier Executives, Star Alliance Gold, and then it proceeds by boarding group 1-4.

As a *Silver, you will be in group 1..so definitely still early in the economy boarding process and you shouldn't have any trouble finding space for your bag.

Being in Economy Plus doesn't change your boarding group... you'll be group 1 because of your *Silver status.