Yes, but in a space based fleet, all infantry in an assaulting army would operate this way, making the rapid reaction force idea effectively pointless.
This is why I suggest drop pods as opposed to drop ships, ten times as dangerous but get you there ten times faster, allowing you to be "drop troop" and lord it over the regular grunts.
I think "drop pod" and "drop ship" are really just semantic arguments and technical details. The point is you're talking about troops infiltrating enemy orbital defences and rapidly entering the atmosphere to land at specific target sites and immediately assault the enemy.
The point is, only the specialist forces actually do the entry assaulting. Their job is to secure entry points for the remainder of your force, who come in safely, and only entered combat once deployed to the front lines.
Whether you're talking D-Day, the invasion of Afghanistan, or the assault on Beta Centurion VI; the general process is likely to be the same:
1. Surveillance
You check out the target area, assess the enemy's positions, and determine an assault plan.
D-Day: Aerial overflights, Special Forces, French Resistance
Afghanistan: Special Forces, Satellites, Aerial overflights
BCVI: Deep-space scanners, Satellites, drones
2. Assault
A small portion of your force, specially trained and equipped, enters the theatre of operations under contact with the enemy, destroying entry-point enemy positions and securing a beachhead for follow-up forces.
D-Day: Beach landing forces, paratroopers, glider-borne troops
Afghanistan: Helicopter assault, paratroopers
BCVI: Dropship/Drop pod assault
3. Invasion
The follow up force exploits the secure beach head to move large volumes of equipment and personnel into theatre, at which point post-beach head operations can begin.
D-Day: Mulberry harbours deployed to Omaha and Gold beaches, capture of Cherbourg, establishment of airfields
Afghanistan: establishment of Camp Rhino, capture of Bagram and Kandahar airfields, establishment of supply routes overland through Pakistan
BCVI: Deployment of in-orbit space docks, surface shuttle ports
There's no way the Allies could have deployed all of the troops needed in France via landing craft or parachute, there's no way ISAF could have deployed all the forces needed in Afghanistan by helicopter, and there's no way a future force could deploy all the forces needed to capture an entire planet by drop ship.
The vast majority of your forces in a space scenario would be deployed into theatre on huge interstellar transports that can't enter the atmosphere, but instead dock at space ports where men and supplies are then transferred to surface shuttles.
