You'll have to check your local laws as to what's allowable. Some states are very restrictive about swaps you're allowed to perform (same manufacturer & model year for example), others don't care as long as the tailpipe sniffer shows clean, and others don't have testing at all.
Generally if you carried over all of the emissions equipment from the original car, and it's functional, and you're tuned well, you might be fine. I don't think cats were mandatory until '75, so hopefully Phoenix's requirements are fairly lenient on a '74, and you can get a waiver as long as the results aren't too horrible (as long as you show you spent a certain amount of $ to fix the problem). Personally I'd call whatever office in Phoenix runs your emissions program and ask them.
Like @jozsefsz said, carrying over the equipment you can will go a long way.
If you want to make it 100% street legal though, its honestly not that hard. There are 351W 4-bbl intakes out there with EGR provisions.(OE and aftermarket both, early-to-mid-80s full-size Ford cars and pickups were available with 351Ws with 4-bbl carburetors and EGR, and I believe Edelbrock is still making an intake for them with EGR, I know they are for the 302) I've never seen a V8 II with a smog pump, so you probably won't need one of those. As long as you've got a PCV valve, and EGR valve, you're legal in most areas, a few others will require a factory-style air cleaner, pre-heater tubes, and possibly catalytic converters, and all but the catalytic converters are easy bolt-on affairs. There's no reason you couldn't be pushing 350hp or so from an emissions-legal 351W if you really wanted to using off-the-shelf parts.
If you're just wanting to swap a V8 in general, a 302 will be a bit easier (they're a little narrower, and a little shorter vertically), but a 351 can be and has been done.
The easiest rule-of-thumb to follow for any engine swap is to make sure the donor engine is from the same year or newer than the vehicle it's going into. If you do that, and keep your existing emissions system components or the equivalents from the newer engine, you'll have no problems passing even California's testing if done correctly with everything functioning. (Although you may not be able to go as far with performance parts as you would in other areas.)