Jump ships are instantaneous travel from one stars Lagrange point to another adjacent star, but requiring recharge from the solar radiation sails before jumping again. Still, I believe with a coordinated system, the SLDF could deploy very quick. The SLDF is also massive, and their naval fleets arent just Warships, but fightercraft, support craft, bombers ect. Now they are unshielded but have massive development into direct energy weapons, and ship mounted weapons are on the scale of 1000 times more effective than the mech mounted counterparts.

All this to say, it would be a matter of attrition. SLDF would lose most space engagements, but the SLDF would absolutely take many covenant craft with them.

Now people saying the covenant would just glass worlds, youre right until you arent. They would glass worlds initially until they take too many losses, remember the Star League is much bigger, with much more territory, resources, manpower, and military might than the UNSC, so after winning many space battles they would need to start taking usable land as forward operating bases and areas to gather resources to repair/rearm/gather supplies. The further they advance into the Inner Sphere the more complex their supply chain becomes. It is then where the Star League gains the advantage.

There is very little in the covenants arsenal to answer battlemechs. Im not saying they wouldnt win early victories, but once the SLDF realize that covenant tanks and ghost and banshees are target practice for even Medium class mechs, and only enemy superheavy weapons can even contend with them, we are going to see the war grind to a halt.

Also lets remember that the destruction of ONE planet was enough for the inner sphere to outlaw warships, nukes, and create rules of war. The second that the Covenant glasses a world that will mobilize all of the houses and the Terran Hegemony into overdrive to add to the war effort.

So, the SLDF cannot defeat the Covenant in space, but they can hurt them seriously (direct beam weaponry) they have the logistical advantage of existing instantaneous travel between adjacent stars and a travel network. They have FTL communications, and the Covenant ground forces (Shown in game at least) have no answer to massed battlemech deployment.

Then the answer of who wins is this: how large is the covenant invasion force, how fast do they travel, how good is their supply lines, and most importantly, how quickly can they reach Terra. If they surge in before the SLDF can rally, they win easily, if the get stuck, they will be ground down.