NAD 3020 a viable option for a quality system?

I'm on a budget, and my system has been evolving for a few years. I look for "overachieving" products; bang-for-the-buck is a big deal with me! What I don't want is to have any component which really compromises the rest of the system.
My current components:
Marantz CD-67 SE
Totem Mites (on quality stands)
Kimber Silver Streak
Kimber 4TC

I can get the "Legendary" NAD 3020 for under $100, but am wondering: Was this amp merely "good for 1980", or does it still challenge contemporary options like the current NAD's or Arcam Alpha 7R (which I can also get a good deal on).
Under $100 for a 3020 in good condition is a good deal. Amps have not really gotten better since the 80s; "modern" ones just have more power because most (not all) modern speaker need more.
The NAD is great, but you get what you pay for. My first amp was a 3020 : it's a great amp, but a bit limited in dynamics, and with a slightly "fizzy" treble. When I upgraded to a Cyrus 2 integrated amp the dynamics and top end improved markedly. I bought that amp used for about $250 about 7 years ago. I think the NAD will be the weak link in your system, and you will not be happy with it in the longer term (however you'll be able to sell it on for the same amount of money, so this isn't a problem).

That said it's all about budget, and I think you'll have to spend considerably more than $100(at least $300) to get a big improvement in the sound. I don't think a newer NAD or Arcam (for around the same price) will sound much different. I think you'll have to jump to the next league (Audiolab, Cyrus, Linn, Naim Nait, bigger Arcam) to really notice a big difference in sound. Audiolab 8000As are about $350 used, and are leagues above the NAD, but they're 3 times the cost. The Audiolab or Cyrus 2 would be my choice (the Nait is a lovely amp, but overpriced on the used market).

If you do get the NAD there's a great tweak which worked well for me. Unplug the jumpers between the pre-out and power-in and connect the CD player to the power in. The sound was much more punchy (less warm and mushy). I have the same CD player as you and I know the volume resets to max when it's turned off, so you'll have to be careful. To me this implies that the NAD's preamp is the weak link, so I would discount using it in a pre-power setup later on. If this is not convenient then at least replace the jumpers with a quality interconnect ... that also helps, but to a lesser degree.
I had and enjoyed a 1020B/2155 combo for many years (the 3020 separates equivalent) and think its one of the great bargains in low/mid-fi audio. However, neither of these pieces are especially fast, accurate or resolving, but rather produce a soft, warm sound that takes the edge off things and can make an inexpensive system sound wonderful. Depending on your tastes however, in a better resolving system these may not be the most complimentary pieces.

Keep in mind that the equipment is also 15 years old and was not built with the highest quality parts to begin with. Any amp you find now will likely be showing its age and won't provide quite the same quality sound it had originally. Still, the amp and preamp I had continue to be used as a bedroom system at a friend's place, so there's something to be said for the way NAD used to build things.

BTW - Both the 1020B and 3020 achieved "legendary" status because they were great pieces of low/mid end audio gear. This doesn't, however, elevate them to the level of modern high end audio equipment. They're worth having for a second system, but are a bit outmatched with today’s high resolution sources. Nevertheless, $100 is cheap enough to experiment with, so it might be worth giving it a try and see what it does with your CD player and speakers.
My first quality audio system featured a 3020, I still have fond memories. Sold it to my brother, now I kinda wished I'd kept it. The 3020 represented value unlike anything I've stumbled across in audio gear (well, include the B&W DM302's in that category). I know you're on a budget, I just can't see how you could do better for the price. I often chuckle, seems most of the affordable stuff on the 'Gon is either tweaks or bulk wire, kudos for coming across a quality component for a reasonable price.
Guess I'm in the minority. I think the NAD 3020 and it's variations are a true quality product. Mine is 3020B (the 3020A differed in that it had a mono switch on the front and a a MC/MM phono switch on the back) and I have driven everything from Thiel 1.5's, Rogers 3/5A's, Spica's,. It's an excellent budget piece to build a budget system around. On ebay one for $100 would be a good deal. Most go for more.Audiophiles appear to be catching on to an underated piece of yesteryear. On any level of audio you can always do better. The system in my dedicated listening room consists of Quad ESL's/Kinergetic Subs, Berning amps,NYAL preamp. The one in the den is NAD 3020B,Harbeth P3's,Sonograph Turntable Beta Arum Cartridge,various other sources. Musically satisfying? You bet. If your on a budget you certainly can do better. But,the trick is, not do worse on the same budget! Remember, reveiwer's review, consumer's consume! Good luck!
No .. I agree with you trebleclef ... but you can do a lot better for not a lot more money (audiolab 8000A, Cyrus 2 spring to mind).