Grumpy_Mike:
No not in any way. If you make a transmitter without a license to make one you break the law no matter what frequency it is on.
If you operate a transmitter on a frequency you are not licensed to use that is illegal.
Beware of the so called license free bands, you can only operate type approved equipment, not home made or home modified to increase the range equipment.
Actually, Mr. Grumpy pants, if you're a licensed amateur radio operator, you're allowed to build all the transmitters you want (and use them) as long as they're not causing interference or noise on bands you're not licensed to transmit on and as long as it's on the bands you're licensed for.
Quit shooting down this persons dream and ruining their fun and curiosity. There used to be a ton of hams willing to teach curious young people how to build radios and stuff now it's just a bunch of angry old dudes that say "go buy this or that radio" among a whole other slew of things they say you need. This person is obviously asking about radio, probably with an interest in amateur radio.
So my advice? If you don't have an amateur radio license, go study and get your license, buy a cheap 30 dollar baofeng to learn how to practically operate and maybe get some help from more experienced hams, then build yourself a ham set. Use the arduino if by then you still feel it's the best, it's not like you can't filter the fuck out of it just like we do on crystal radios, built by hams for ages. Just look at the crystal tuna tin and tuna tin 2 or the michigan mighty mite. All using crystals, all square waves, same harmonics problem but the difference being that your frequency is immutable, stuck on that single crystal, or however many crystals you have. Your cost won't be a lot different for either of these radios. A bag of crystals is around 5 dollars on amazon. An arduino clone is about 5 dollars. The challenges are the same, the way you work them out will be roughly the same. It's up to you how you implement your radio. Just please do filter your circuit output so that the rest of us don't hear your transmissions anywhere other than where they're supposed to be.
Screw what these guys have to say, honestly you've got me looking at arduinos as an alternative to crystals because they're flexible and I have 3 of them. Thanks! Message me with updates and maybe we can collaborate on this. Also, don't forget crystals as an option, or if you're set on a chip, TI makes synthesizer chips that are already proven for such an application...maybe one of those could more effectively create the frequency desired and then be controlled via arduino.