I am not going to spend the time looking up the parts as you could have posted the links but it looks like it will work if the software is written properly.
SDA is directly connected to A4, SCL to A5. The redundant SDA/SCL pins are a convenience when using boards that have the I2C pins on something other than A4/A5, such as the Mega, so that a shield designed for an UNO will work properly without having to run extra wires.
That would often be a waste, since pins 2 and 3 are the only ones that support external interrupts. Those displays are "bit banged", you can use any digital pins at all to drive them. Even, A0-A3 (you're already using A4, A5 as noted.
Don't forget the modifications (Google it) to the RTC if you run it on 5V, or the module will apply charging current to the non-rechargeable battery, which could start a fire.
Right about the power supply, but wrong about the I/O connections. If you do that, then you have mixed voltages on the I2C lines. The correct way is to either modify the RTC, or use a different RTC.
You need to remove either the resistor or diode here:
The board was designed for rechargeable Lithium batteries. So it has a charging circuit, the diode and resistor. If you try to charge a non-rechargeable Lithium battery, it can heat up and explode. Most people don't use a rechargeable, can't even find or buy one. So it makes sense to modify the board.
The resistor will come off really smoothly, with a soldering iron with a dab of solder on the end. Or just break it off, but then it will be a permanent mod.
You have a 5V Arduino, you have to run the board on 5V so the I2C bus runs at 5V.
(The PDF arrived today. I was dead annoyed with them because they shout about a free manual but you have to give your credit card details to get it. When I complained they sent me the PDF.)