Shields draw a constant 1 MW per second from the sys capacitor while recharging. I noticed this when working on that
ancient shield research thread, and used it to measure the size of a given shield. One megawatt times one second is one megajoule, so that's the unit I assigned to shield capacity. While the specifics and formulas in that thread are now out of date, the unit remains accurate and ultimately caught on. What this means in regards to your question is that as long as your sys capacitor is not empty, your shield will recharge at the same 1 MJ per second. If your capacitor is completely depleted, then your shield will recharge at the rate that your sys capacitor refills (up to one MW per second, naturally).
Since more pips in sys linearly increases the rate the sys capacitor fills (with 4 pips giving you the sys recharge rate listed on your power distributor), assigning more pips to sys
may increase your shield recharge rate if you have a small power distributor. For reference, the vulture uses a class 5 power distributor. The 5A PD has a listed sys recharge rate of 2.5 MW. 2 pips in sys would give you 1.25 MW of recharge, which is more than enough to cover the shield's recharging needs. Anything more than that will not be speeding it up at all.
Note that things behave a bit differently if you shield fails entirely. First, there is a 16 second delay. After that, the shield "charges" up internally to 50%. That's what's going on with the red boxes. Once that is done, the shield will come back online at 50%, and begin to charge normally. This is why switching any boosters off speeds the process up. By lowering your max shield value, you're also lowering your 50% value, thus decreasing the time and energy it takes to charge to 50%.
Yep, 4 pips on Shields makes them stronger, dont remeber by how much % exactly... few Cmdr's did tests with shields, and it was something around 50% stronger.
Having 4 pips in sys (vs. 0) effectively makes your shields about 2.5 times stronger, actually (they basically negate 60% of the damage done to them). It makes a huge difference.