Imagine one to three persons going back in time to a society like that of the Roman Kingdom (the period before the Republic), and they attempt to reform as well as modernize to an extent (up to the technology of the late 17th Century), but improve hygiene and sanitation to the same amount as the late 20th. Would this be possible in at least 100 years? Let's say the individuals are highly educated in many fields and most of the time will be spent on technological improvements and hygiene and not so much on things such as criminal justice. Let us also assume that the territory has all the resources required and has a population of two million. And they also easily manage to gain control of the kingdom within 10 years and there may also be magic. Would this idea be feasible to be carried out if there was a proper plan?
Technological reform without social reform can be less than successful.
You know why we call plumbing by that name? The word literally comes from the Latin for Lead; they used the metal for their water management throughout the empire because it was cheap, malleable and easy to manage as a resource. There is some evidence available to say that the Romans actually knew lead was toxic, but they still used it because it was too (in a word) useful to give up.
Arguably, we could say the same in the modern world about single use plastic shopping bags. In Australia, we've just recently had one of our last states ban their use. Shopping bags have been touted as the cause of much pollution in the ocean and have been seen as a massive impost on consumption of petroleum products for their manufacture. These have been known issues for decades, but it isn't until there is a compelling drive at the social level to change that we see action on these things.
The same will be true if your time travelers come back with technology alone. Taking gunpowder back to Roman times may well be a game changer and it is the sort of thing they may embrace, because their legions were always looking for advantages in combat and it was a big focus of Roman life that their army was (more or less) unstoppable. But, did they really see healthcare or hygiene as a priority? Well, they were still using toxic metals to route their water supply, so probably not.
What will make your empire grow, what will really improve the lives of its citizens, is education. Sure, put gunpowder out there as a gesture of goodwill and get your name established as someone of influence, then use that influence to redirect education into STEM research as well as the humanities. Building these two in concert allows you to change community sentiment to best take advantage of the technology devised through STEM research, and it also means that removing lead from Rome and other large cities in the empire could be justified as an expense when the people demand it as they understand the cost to them personally and to their empire.
Ultimately, what I'm saying is that the only way the introduction of technology allows an empire to grow is if they're ready for the change that such a technology can support and actually want it. Otherwise, introducing technology blindly means it is likely only going to be used in a destructive way because that allows for those with that technology to have an easy or cheap capability of building power over others. To use a technology for good, a society must be able to see the need for a more inclusive set of goals that extend past selfish desires. That requires far more than technological advancement; it requires social advancement.
The answer to your question therefore is yes; it's possible but only if your focus is social change, and you are careful to only introduce new technologies as the society you're building is ready for them. I have no figures on how hard it is to change the mindset of an ancient Roman (having never tried it before) so I have no idea how much of an effort this would be but my focus would start not with the senate, but with the mob. Get them demanding reforms as a groundswell base in Rome itself and you might be surprised at how quickly things change.