Short answer: NO.
Medium answer: MAYBE, with a time machine.
The basic issue here is one of chicken and egg and which came first. While, with chickens, we really do not and can not actually answer that question, on account of it being philosophical...
With languages, and especially with invented languages, and most especially with a posteriori invented languages, we can answer the question, and that answer is NO. The rationale is fairly straightforward:
- Glosa is an invented language; it is based on Interglossa, another invented language: it can not, therefore, have existed prior to its antecedent (this is what it means to be an a posteriori invented language)
- Interglossa itself is grammatically, and as I understand it from a quick glance, an a priori invented language, though its lexicon is taken from Greek and Latin as you say: although its grammar could have (probably) been invented at about any time in history, its lexicon can not have existed before the Latin and Greek languages existed
- Greek & Latin are the natural languages upon which Interglossa and eventually Glosa are based; without both of these languages existing, neither of the later invented languages could be made.
As you can see, anything made using a pre-existing component can not antedate the existence of that component. You can't be born before your parents were born; a modern smart gadget can not be made before there is a network for it to be smart in, or the plastics or computer components it's made from.
Reality Check:
The final piece to the puzzle is the actual idea of inventing a language in the first place. While it's true that the divine Claudius was something of a neographer, having invented a few novel letters for the alphabet, we don't really have any evidence for anyone making languages on their own at that early date. The first invented language we have evidence for is Lingua Ignota, and that appears in the 1200s as an ecstatic religious & spiritual extension of Latin.
A few centuries later, we start to see people deliberately and systematically creating new languages, and these were what we now call philosophical languages.
Interglossa and Glosa are what we call International Auxiliary Languages, and they arose during a time when Europeans were struggling with national identities, when the world was becoming smaller (due to rapid communications with telegraph and telephone) and the mass movements of peoples. The idea of the IAL can only exist when people not only recognise the validity of other people's nationality (and the national languages spoken in those countries) but also the validity of the need for true understanding between peoples of differing nationalities & languages.
The earliest sensible time frame for something like Glosa to be devised is therefore in the mid to late 1800s. And of course, this would mean that Interglossa's invention would have had to be moved back also to the mid 1800s or so.