I know this is an older post, but I'd argue they did clash.
Zhukov's 1st Byelorussian and Koniev's 1st Ukrainian Front's ran into each other in the streets of Berlin.
Without making this post too long, I'll briefly summarize the main dates and what happened. My sources are derived directly from Chuikov, Koniev, Popiel (Ops Officer 1st Guads Tank Army), accounts, German accounts, and a 1994 documentary called Berlin at All Costs!. The documentary was particularly revealing as it was filmed in the Moscow military archives and Russian Staff Officers were actuallying showing the battle log that coroborated the clash of the two Fronts.
16 April - "Berlin Strategic Offensive Operation" is launched.
17 April - Koniev clears the German defensive zone with the 3rd Guards Tank Army and orders it to drive toward Berlin - they actually had sealed orders already issued to head northwest into the city
20 April - Zhukov clears the final German defensive zone and begins his drive toward Berlin
22 April Koniev's 3rd Gurad Tank Army reaches the Teltow Canal, beating Zhukov to Berlin - the interfront boundary runs straight to the Anhalt S-Bahn Station
24 April - The 1st Guards Tank Army reaches the Teltow Canal and finds out that Koniev's forces are already there. An upset Zhukov orders this fact to be verified immediately
Sidebar: Zhukov sent nearly 1M soldiers headlong into Berlin . . .Koniev was driving north with close to 100K, neither of their actions were coordinated at all.
25 April - Zhukov finally accepts Koniev is in the city, and against all military reason does two things: 1) he orders Chuikov to cut across Koniev's line of advance and the Stavka interfront boundary to cut off Koniev physically from reaching the Landwehr Canal (btw, he didn't tell Koniev he was doing this) and 2) he orders operation "Salute" a massive air assault within the city.
26 April - Koniev forces radio in that they are being attacked by Soviet aircracft all along the front.
27 April - German forces in Steglitz and other southern districts report the presence of Koniev forces just a few kilometers south of the Landwehr Canal
28 April - Chuikov launches an offensive across the Landwehr Canal into the Government Quarter
28 April - Koniev launches his offensive to reach the Landwehr Canal
28 April - The 3rd Guards Tank Army supplemented with infantry divisions from the 28th Army runs directly into Chuikov's forces stopping Chuikov's assault cold- runing street battles between both Soviet Fronts occur that cause fratricide.
29 April - Stavka steps in, pushes the interfront boundary further west and Stalin personaly asks Koniev to leave Berlin and prepare for an offensive toward Prague.
According to Senior Russian Staff Officers interviewed for Berlin At All Cost! Koniev's forces actualy crossed the Landwher Canal and took the Anhalt S-Bahn Station before Zhukov. I might argue that this didn't happen, but I am confident based on the material I accessed that both Fronts did clash in the streets of Berlin. Koniev himself is pretty open about this in his memoir. I detail all this in Bloody Streets.