So...it takes that one bar signal and transmits it to the other room as a one bar signal?
Oh, you'll get a stronger signal... but like the old saying goes, garbage in, garbage out. No matter how strong the booster unit gives you inside the house, it is at the mercy of the source connection that the window unit can get. That window unit has the advantage of being powered, so it can crank the ol' gain on its internal amplifiers, but if the signal it gets is weak, you ultimately end up going over that connection....
These boosters do a couple of important things.... they provide a strong signal to your phone so your phone's transmitters don't have to increase the amount of power being used to maintain the connection. And it also helps extend the signal throughout the house (T-Mobile's wavelenths don't penatrate walls all that well). They don't miraculously take a weak or poor signal and turn it into something that seems like you are parked next to a tower.
Let me explain it using how it works at my house:
If I turn off my booster (and disconnect from WiFI), I get a somewhat poor signal... -110dBm or so, with a low SNR (signal to noise ratio). I get LTE in certain spots, but that often drops down to HSPA in parts of my house. Voice calls get that familiar digital stutter in spots. If I stand on my porch, where my signal is best, I get LTE data speeds in the mid to high teens. And when I look at battery stats, my phone signal can consume up to 25% of the power used over the course of a full day.
If I turn on my booster (which sits on a table on the afformentioned porch), the window unit gets 2 or 3 bars of LTE (out of 5). My booster unit shows an ideal connection to the window unit. My signal is 25 to 35dBm better, which is a huge improvement, with a much higner SNR. I would maintain an LTE connection throughout my house (and a decent amount outside)... and if I look at my battery stats, my phone radio draws a fraction of the power it did when it had to communicate to the remote tower directly (about a 1/3rd or less). Voice calls are clear, steady and reliable.
BUT...... if I do a speed test.... I pretty much get the same up and downstream speeds as I did without the booster, standing in the same spot as the window unit. No matter how much the signal is boosted, its still, at its heart, a weak signal and subject to the issues that a weak signal brings (i.e. lower data speeds).