As the title suggests I am interested to know if doing a few repetitions with moderate or heavy weights multiple times a day is as good as a "normal" workout. For example doing three weighted pullups then waiting an hour and doing three more and so on. Assume that maximum amount of repetitions with the weights is around 6.
What you're talking about is essentially Pavel's Grease the Groove training. The idea being that you take about half your max reps, and do lots of sets throughout the day in order to train the body to be more efficient with the movement.
When you say "will it be as good as a normal workout", that depends entirely on your goals.
For strength, it should be better than a normal workout, you should see your weighted pull up strength increase quite nicely.
For muscle gain, there's likely to be some, but not as much as if you were clustering the sets together to do something like 3 x 5 with a few minutes rest between (this is what all the training literature tells us, I haven't personally measured the difference in muscle gain between the two).
For fat loss, again, there may be a little compared to doing nothing, but it's not going to have anywhere near the effect of a more exhausting training session.
Depends on your goal. I'd generally say that GtG (Grease the Groove) is only practical if those weighted pull ups are rather low RPE (rate of perceived exertion) or you have many reps in reserve (RIR) and you only use the technique for relatively short bursts of time (<2 months) for any given lift.
As Dark Hippo pointed out, typically you'd take about half the number of reps you could do and focus on executing them with excellent technique. The reps should be very clean looking with no grinding. Grinding reps will hurt your progress with GtG. Going to failure won't work with the technique, you'll burn out pretty fast.
For example: If you can do 6 weighted pull ups with 25 lbs, you'd do sets of 3 with that weight (3-4 RIR). Or less than that if you start to get fatigued after multiple sets. You really have to pay attention to how cleanly your reps are executed and ensure you don't grind. Long rest intervals would be advisable here. Which is often what happens if you spread the sets out over the course of the day.
It's more often used with calisthenics when spread throughout the day (i.e. 20 reps of pushups several times a day, when your max is 40), but that's only because working up to heavy loads on say a squat/deadlift without warming up comes with risks. It's also more typically done at a higher frequency, but lower volume (i.e. 2 sets of 3 or 2 sets of 5) when you do use heavy weights. For instance Pavel's 2x5 program.
The former is an excellent way to improve technique in calisthenics and the latter improve strength quickly. Generally the believed benefits are tied to improved technique. However, low volume ~4 RIR training will reduce fatigue, improve recovery and let you train more frequently as a result too.
It is generally not a great way to build muscle mind you, because you want to get more mechanical tension and GtG is a way to avoid too much mechanical tension/fatigue.
When used at higher reps, it can be effective for fat loss so long as an energy deficit is present but I wouldn't say ideal. Heavy weight training will help preserve muscle mass better but using a technique with more mechanical tension and fatigue every other day or 2x a week would likely be more effective overall for that goal too.