Of course.
That is because faking/obtaining a document that show that you actually passed elementary school is not a easy thing. She could have tried but she was never a person to do something so illegal. After her last surname change/add-on she lived under the name Niko Sagar for a long time (and her last surname change was long before anyone actually started caring about keeping the records of names and surnames of commoners) so she had little trouble with her identity (she would just register a daughter named Niko using a illusion of a child and would take over that identity when the "new" Niko's age reached adulthood).
Most of the "Workshop" is just a complex magical structure, but the storage space and "Reactor" are located in a different plane of existence - one created by Traveler and integrated in the "Workshop" to allow roughly 1,000,000 km3 of storage space plus enough room for the "Reactor", magical circles that make up the magical base of the "Workshop" and storage for the fuel powering the "Reactor".
Like mentioned above, the "Rooms" that have a storage ability store it in the mentioned different plane of existence. Note that due to massive magical circles attuned to deities/spirits related to weapons and/or warfare the "Arsenal" usually just copies weapon (and ammunition) instead of actually taking them out of its storage space, to allow the user increased firepower (by creating multiple magic-manipulated copies of the same weapon) if the user wishes so.
The "Workshop" is meant to be provide all the needs (and does that pretty well) a mage might have - for combat, items, tools or calculations trough the "Arsenal", "Forge", "Warehouse", "Crafts" and "Calculus". The fact that is was meant for a mage is show in it rather draining stamina then magical power from the user - a mage would usually not really on stamina in combat but rather on magical power to cast spells while being aided by the "Workshop" to increase his damage output/area of bombardment. As for the two other functions; the "Gate" is an emergency solution for dire situations and the magic replenishment of the "Reactor" is not actually meant for human usage altogether due to the possibility of overloading one's magical capacity - which causes damage to the neural system. The ability to channel magic out of the "Reactor" into the real world is meant for restoring magical power over large/massive areas, to power up magic-driven devices or to provide power for large-scale rituals which usually require multiple mages without the need for more then just the caster.