On the ICE 517 from Mannheim to Munich (you will change trains from ICE 74 to ICE 517 in Mannheim) there is a paid Wifi Option in the 'HotSpot' marked areas on the train.

So, you will have internet access on 50% of the trip going by ICE, you might consider taking the EC which arrives almost 2 1/2 hours earlier and then use the internet in Munich afterwards.

4 hours 12 direct vs. 6 hours 32 (+ change of train in Mannheim), i would take the direct train.