I have not experienced this with a Hilleberg, but my Marmot has similar inner material. One time in Norway it was really horrible weather with heavy rain on the outer tent and clouds that were not only floating around outside my tent, but also inside the tent. There was tons of condensation on the inside of the outer tent. A lot of that even started dripping on my inside tent and when I woke up the next morning a small puddle had formed on top of my inner tent. The moment it was disturbed a stream started leaking into my tent.
To answer your question, yes the inner tent will protect you from some water as long as it comes very slowly and gently. Anything but the lightest rain will not be stopped by the fabric. And even with very light rain, as soon as you touch the fabric, the water will come flowing in until it stops raining.
In your case you'd probably be better of with a poncho shelter and maybe a small net tent.