Orbit doesn't work like that. Getting 200, 300 miles up is the easy part - the vast majority of the required energy comes from going sideways at 7800m/s.
In exchange for that, you have to build your rocket and satellite to withstand 10,000 gees of acceleration and hypersonic flight through the lower atmosphere. And somehow build a rail gun that can fire something the size of an office building.
Firing sideways could save you much more fuel but also means you’re in the lower atmosphere at much higher speed and for much longer.
I think I'm taking a lot of liberties to imagine a future where we figure out a ton of challenges to get all the engineering to match the theory of making this happen. And in general, I believe we should take an optimistic approach to the future, given that getting humans into space in scale would be a marvelous accomplishment for the human race.
If you mean "account for the sideways movement" as "give the satellite the horizontal component of the required orbital velocity" this doesn't work for a variety of reasons - #1 is that the railgun is 2000m/s and orbit is 7800m/s, and #2 is that things going 7800m/s (17450mph) at or near sea level tend to get very, very hot very, very quickly which is not particularly great for railgun projectiles and utterly disastrous for things like solar panels.