A surgical strike and being fast is the best way to achieve mission success. I agree they might not get most of the leadership but if they can establish a cordon around the arena they should get quite a few. The arena seemed somewhat isolated from the rest of the surface forces.
I don't think the Battle Barge can take on whatever Separatist Navy Assets are in system. The Republic brought in a pretty hefty fleet.
Arena is the worse place tbh, there are droid Factories that were connected there and according to the expanded material those were producing hundreds of thousands (likely a day) they'd quickly overwhelm the Spacemarines through chip damage.
Battle Droid blasters contrary to popular belief aren't entirely ass they should be roughly on par with a las rifle or slightly stronger setting of a las rifle.
According to BFII the E5 has a fire rate of 300 rpm, according to the Clone Wars a single Separatist squad has the following composition
48 B1 Battle droids (Not counting Superbattledroids), that's gonna be roughly 205 blaster bolts a second even with 50% accuracy that's 102.
How many blaster bolts can a Spacemarine realistically take without low-balling blasters? 5 seconds, 10 seconds, a minute worth? A minute would literally be a thousand blaster bolts striking them surely that'd have compromised their armor and vital organs by then?
What about the Spacemarine weapons? The Spacemarines carry 30 rounds on their bolter, how many magazines will a Spacemarine realistically carry, 10-20 magazines?
Let's say 20 magazines x 30 bullets so 600 rounds per Spacemarines. Each individual droid factory (likely hundreds of factories) on Geonosis can build between 66 (lowest end) to 1,200 an hour (highest end) and the maximum amount of ammo the Spacemarines will realistically have (240,000 rounds) would only allow them to be able to destroy around quarter million droids before resorting to melee.
And the droids will be able to literally build faster than the Spacemarines could destroy the droids. And without aerial superiority all the drop ships are getting shot down. So the Spacemarines will have to be extremely frugile with their Librarians as they'd be their only way to leave the surface alive.