The heater voltage is definitely important. Too high and it burns up the tube, too low and it has another sort of issue.
It has to do with how a tube operates. The orange glowing rod you see in the tube is the cathode. That cathode is heated by the heater. The heater and the cathode are only separated by a very thin insulation. The cathode has a very high current flowing through it and it can only boil off so many electrons no matter how hot you get it. Too hot and the electron emission comes to a saturation point ( it won't boil off any more electrons ) and the insulation between it and the heaters will break down causing a short. If the heater voltage is too low and the cathode is too cold it reduces the ability of the cathode to boil off electrons, which actually increases its life, BUTTTTTTT it is sort of a ratio. The heater voltage and the plate voltage have to scale together if you plan on going with a lower heater voltage. If you lower the heater voltage too much and the plate voltage is too high, it has a similar effect as having too high of a heater voltage. The cathode will build up more electrons than it can boil off and it can arc/short to the heater and or break down the cathode's coating. Either way, the tube's life can be shortened considerably.
Since using a variac will draw down the entire amp, the lowered heater voltage is not generally of issue unless you have a power tube that is sensitive to heater temperature. The power tubes are the tubes generally most sensitive to heater voltage. Which makes sense, as they are the ones with several hundreds of volts flowing through them. I think in 90% of cases, using a variac set to reasonable levels of voltage reduction is of little issue. I think 90 volts is probably the lowest practical voltage you can set one though. I think with most 100 watt amps, setting it to about 90 volts reduces the amp's output to about 30 watts. I would say that for everyday use, keeping it closer to 100 volts is probably a safer bet. Most consumer products are rated for somewhere between 110v - 120v, many landing at 115v. A 10-20 volt drop is of little worry. Beyond that, you start getting into murky waters.