I can't give you any kind of exact details about what to expect in the way of race related traffic, but can observe in general you're right to be "worried." This is particularly true since I-74 joins I-465 at just about ground zero for race related traffic.
My gut says for your son plan to just plan on avoiding the entire area. This is for two reasons:
1. Doesn't add too much time overall (more on this in a moment) and, more importantly, the extra time of avoiding the area should be pretty constant. That is, it is fairly predictable (to the extent that anything driving related is predictable); unlike what might happen with race traffic. In the best case, race traffic might not be too bad and only be a minor slowdown, but in the worst case it could be a total nightmare and add significant time.
2. To me the real problem with going through the Speedway area (hoping it won't be too bad) is that you won't know it *is* too bad until it is too late to do anything about it. Once you get into it (and it's bad), there won't be any option but to continue and any alternatives that might be possible will *also* have race traffic involved.
Those are the main reasons I suggest just planning on using an alternative route. Here's a few ideas:
1. Swing over to I-65 well before hitting Indy. A *really* quick glance at Google maps shows State Road 32 (from near Crawfordsville to Lebanon) would be an option.
2. At this point I-65 through downtown would be one option and as long as it's not right when the race was letting out, shouldn't have any problems at all. Even if the race is letting out a good chunk of it is still inbound from the standpoint of the race.
2. Another alternative which will pretty much completely eliminate the Speedway traffic as an issue is to swing around the north side & west side on I-465. This would start on I-65 (see above) and then simply go clockwise around Indy (rather than counter-clockwise).
As far as time differences of these routes:
1. Google maps shows the I-74/SR 32 interchange to I-465/I-65 interchange as ~50 minute drive. This is the base line for comparison as it's the time if the race wasn't going on and/or if you can sail through without any race related traffic.
2. Google says taking SR 32 to Lebanon and then I-65 through downtown comes out at ~60 minutes - only adding ~10 minutes - well worth it in my mind.
3. Taking SR 32 to Lebanon, I-65 to I-465 and then I-465 around the city (north & west side) comes out at ~70 minutes, only about 20 minutes more than the base line.
In my opinion taking either of these alternatives - which I can't imagine adding more than 30 minutes at the worst (I've bumped up the Google estimates) and perhaps as little as 10 minutes would be well worth it as they all but eliminate the chances on a delay due to the race.
Even if a race related delay added 15 minutes (and it could be worse if there is a major issue), that the average of the additional time of the two alternative.
Furthermore, I personally would rather add an extra 15 minutes due solely to greater distance (i.e. traveling at regular speeds) than I would an extra 15 minutes plodding along in heavy stop/go traffic.
That's my $.02, hope it helps,