I picked up a used center speaker to use as a surround back speaker in a 6.1 setup. Being the idiot I am, I never thought to check the specs before I bought it. It turns out this is an 8 Ohm 35 Watt speaker. My receiver puts out 600w at 100 watts/channel. Considering it will be used as the back speaker, I didn't think it would have as much coming out of it as say the two fronts. Is there any harm to hooking it up anyway?
For a start, don't beat yourself up for not reading specs. It's an easily overlooked thing when you're starting out in home audio. Many people do not even caution themselves by reading them at any point. At least you thought about it post sale.
It seldom does harm to any of the components, where the amp has sufficient headroom to drive speakers rated at much less the suggested output of the amp; the caveat being always: within reason.
It is when speakers offer a larger load than the amp is happy handling, that the most harm is done.
In this case, it seems you are clear on the wattage side of things. I'd say it's more important to check that the impedance matches between the amp and the front speakers than anything else at this point.
35 watts printed on your speaker is little indication of 'how much sound' it will produce. Rather, listening to see that the setup pleases your ears is a more even test.
What is also worth looking up, is what the combined load from all the speakers in your setup present to the amplifier, rather than just taking each pair into account seperately. With a 600w amp, I somehow doubt you'll run into trouble along this front.
I'm a bit of a stranger to 6.1 - well, any surround system, as I personally prefer 2 channel amplification - so there will be others with more detailed advice along shortly, I wouldn't doubt.
But as a rough conclusion, it seems it will do no harm to 'try it' as you suggest.
You are certainly not an idiot, and I wouldn't lose any sleep over this. As long as the speaker is not audibly distorting it will be fine.
Many mass market HT receivers are rated at 100wpc with only 2 channels running. When all are running the produce substantially less wattage per channel (This is not true of higher end receivers that will give you 100wpc through all channels).
Additionally, most 6th channels (i.e., rear center) are more ambience and fill in between the two rears. They don't usually have anywhere near the volume/wattage that the front left/center/right do. Unless of course you are watching Lord of the Rings and then all bets are off.
Since it is a center channel, and is probably small, make sure the receiver is set for that channel as "small". If you can set the crossover for each channel individually, set it up slightly higher for this speaker (say to 100hz). This will send the bass frequencies under 100hz to the subwoofer. Since the bass will be minimal in that speaker under these conditions, it will have a much easier load, and minimize the chance you will damage it.
In any case, as long as you are not driving the receiver or speaker into distortion, you will be fine.