Would it be acceptable and/or effective to do Wendler 5/3/1 daily rather than Mon-Wed-Thur-Fri?
I don't necessarily mean more effective, I merely want to do it for enjoyment sake. But I need to know if it would likely stop improvement.
Wendler 5/3/1 is designed around certain assumptions, and until you know how your body responds to the stimulus that the program provides you really don't have a foundation of knowledge of what the program isn't doing for you. There's already a great deal of flexibility in the program, but training 7 days a week is not within those constraints. Wendler recommends you do the program as written for at least 4-5 cycles before you start making it your own. He has a book called "Beyond 5/3/1" that is a collection of variations for different goals.
Now, an option that is very much compatible with the tenants of 5/3/1 that would have you doing something every day would be something along the following schedule:
Conditioning might be doing a barbell complex, using a prowler, running hill sprints, etc. This is heavy conditioning, and it should be short in duration. For example, 20-30 minutes would be more than plenty. If strength training suffers, dial down the intensity of the conditioning work.
Active recovery is doing light activity that raises your heart rate a little, but keeps it low. For example, a relaxed walk around the neighborhood where the heart rate doesn't go much above 120 BPM.
Why 5/3/1 Strength Training Doesn't Work 7x a Week
The problem with taking something designed for 4 days a week max and then applying it to 7 days a week is that it throws off the overall volume of work for the week you need to do. If you do too much volume, your body will get too fatigued and you'll likely see your progress going backwards. This is particularly true because 5/3/1 has you doing AMRAP (As Many Reps As Possible) on the heaviest set. That means you'll be maximizing volume every session. It's designed to let you recover properly with 4 training days a week, but not more than that.
Training 7 days a week is fairly common for Olympic weightlifters, and is one of the tenants of the Bulgarian Method. It's important to manage the following:
It's very easy to start to become fatigued training every day. When you start having to psyche yourself up to get in the gym (which will happen), you need to do a planned minimum day. You need to keep doing minimum days until you are mentally refreshed and looking forward to getting in the gym again.
5/3/1 is a very specific program with a very specific goal. If you want to build strength consistently it's one of the go-to-programs. Wendler himself expressly forbids you to tinker with it, though, and for good reason. Once you start increasing frequency, you will probably not be able to keep up with the intensity, which was the whole point of 5/3/1 to begin with.
So I would say no, you cannot do 5/3/1 daily. Well, maybe you could, but it would have to be a watered down, half-assed version of it, as you will not keep up the required intensity if you lift 7 days per week. (Also Wendler hates it when people change the program and call it 5/3/1, so you'd have to give it another name if you change it.)
If you enjoy training daily, however, there's other programs out there that might be a bit more up your alley. Christian Thibaudeau is a big advocate of high frequency training. Most of his programs (example) utilize 5-7 brief workouts per week that are tailored to work at that high frequency. There're probably more, but those are the ones I know about.