Yes, and it got totally obliterated. The Spetznatz fleeing into the forest, the VDV dying on the Hostemel Airport.
Obliterated is an exaggeration, the column of ca 15 000 troops that entered Ukraine around the 28th of Feb. and drove slowly towards Kiev, after 4 days of meeting no resistance it had the 4th of March reached a point 30 km from Kiev and there it stopped and would stay in place until it left in late March. It went untouched for several weeks, and a lot of people were wondering why Ukraine wasn't trying to strike the column (seeing it as a juicy target) with drones, missiles or by other means (Russian air defense systems were protecting the column, and the column had enough artillery with it to make Ukraine think twice about engaging it in artillery duels). By the 11th of March some of the artillery and MLRS from the column had dispersed from the column to take up defensive positions in the general area and in late March most of the column that drove in drove out again. They surely suffered some losses from Ukrainian skirmishes against it, and Ukraine probably suffered losses too in these small confrontations.
The first group of some 700 VDV that attacked the Hostomel Airport secured it from the 300 Ukrainian national guardsmen garrisoned there on the 24th of February but got later in the day repelled by the Ukrainian 4th Rapid Reaction Brigade (some 2000 men with tank and artillery) which counter attacked them with heavy artillery and air support. The next day Russia took the airport with another wave of unknown numbers, Ukraine claimed they killed 60-80 VDV troops in this 2 day battle, we know nothing about the Ukrainian losses. Russia held the airport until they left it to everyones surprise some time in late March (satellite imagery from 28th of March showed that the airport was empty and Ukrainian forces recaptured the empty airport the 2nd of April.
Ok. Then why was the column taking it's sweet time if not for incompetence among the Russians?
If time was of the essence you would think they would take Kiev asap, no?
As I said, I think its main purpose was to cause confusion in Ukrainian ranks, to intimidate Ukraine into accepting the Russian demands, to show that this was no game and that refusing these demands will mean real conflict with Russia. I think they had orders not to go fast, had orders not to engage, they barely utilized the column's firepower in the month it was north-west of Kiev. Negotiations, that begun perhaps because of the column presence close to Kiev, broke down in late March and was the reason why the column was pulled out of the Kiev area, as it was needed on the real front in the east (15 000 men deep within the Kiev Oblast would not have the capability to advance and would in time be overwhelmed if it tried to stay put due to Ukrainians getting organized in defense through massive mobilizations and time to prepare/organize).
So this proves incompetence and that things have not been going according to plan because they should have taken the capital and done so seriously if they knew Ukraine was that much of a threat.
It doesn't prove anything much, I guess it indicates that the Russian gambit on reaching a negotiated resolution within a couple months did not have the desired effect, nothing goes according to plan in war which is why there are fallback plans. If time was of the essence like you say where Kiev would have to be taken quickly (which would have lead a historical city which means a lot to Russians in ruins), then I would have thought Russia would have prepared more than 15 000 men to advance on Kiev when they have 2 million reserves to draw from (of which none had been drawn at all at this point). Cities are not taken quickly unless you have a huge numerical superiority, just look at the battles of Aleppo or Mosul; in Mosul 100 000 troops had to fight for 9 months to take the city against 10 000 insurgents, it was a 10 to 1 numerical superiority (and they also had a vast firepower superiority), the siege of Aleppo was between similar sized forces, 28 000 besiegers against 23 000 insurgents and it took 4 years and only broke out of the stalemate due to Russian air support in the last couple years of the siege. Russia didn't want to have to make Kiev into some Aleppo Ruin, and they still don't want to do that, they still want a negotiated end to this conflict but Ukraine would rather suffer total defeat (forcing Russia to do what it don't want to do tp spite them), or get a total victory (which is close to an impossibility and has been since the start). A quick end to this conflict was never in the cards, and I think Russia was well aware that the possibility of one was slim to none, but they had to try.