I would do a tune on any supercharged setup. I've done datalogs with "stage 1" Harrops where they don't have a tune, and there is a ton of knock retard happening. Which isn't strictly a "the engines gonna blow" issue, but it means you're constantly operating with the safety net of knock retard activating. I prefer to setup tunes where they rarely are using knock retard, just like fuel trims being kept to a minimal, so when you do actually need the truck to pull timing it has the full capability of that safety net to bring to bear. Plus tuning the truck will add in a lot of other features, torque limits reduced so you get the full juice from the blower, MUCH BETTER fueling (stock power enrichment isn't until 70deg of throttle angle, I like that to be max 35deg so right as boost comes in you get enrichment), tire size corrections, speed governor removed, etc. A tune does a lot outside of correcting timing, but that's the biggest issue with a non-tuned supercharger setup. In my opinion Harrop shouldn't even offer that.
And while I'm writing a novel, if you're at high elevation, definitely get a smaller pulley. A supercharger has compounding losses at elevation----the base naturally aspirated horsepower drops, but then the supercharger itself cannot flow as much air (since there's less air to begin with). So you end up with a supercharger that makes less boost, but more of that boost goes to correcting the N/A losses. Your supercharger that makes 7psi at sea level might make 5psi now, and 2psi is used to correct the N/A power loss, so your effective boost (as if it were at sea level) is only 3psi. I am a big advocate of cranking the pulley size, so much so I designed my own pulley setup for the Magnusons (which don't have pulley support like the Harrops) so I could get some semblance of performance out of my TRD 1900 unit (and then people asked me to sell those and now there's a variety of Toyota pulley setups I sell for high elevation people).
My Tundra is a 2008 and rolled 305k the other day and has been supercharged for the past 90k+. It has 35s, 5.29s, injectors, fuel pump, etc. and made 490whp/580tq to the tire and sees full boost every time I take it out. The tune makes or breaks it, and the 5.7 is known to have ring gap issues so you have to run the engine (relatively) rich to keep the pistons cool and stop the ring expansion. If you do that, the engine is extremely reliable even under boost and up to 10-12psi.
