No.
I mean, you can, and if you're soldering it yourself, it's up to you to inspect it.
That looks like one of those DFNs that's impossible to inspect outside of x-ray, so good luck.
You say "high currents for it's [sic] size", but have you checked if the device is not simply rated to handle that current with an ordinary footprint?
Also, what happened to the, soldermask I guess, beside C4?
And why use different sizes and numbers of vias in the chip components? C7 is going to be starved as all the solder wicks into those two huge vias, while R2, C1 and others have one lone via that won't actually affect much.
Also, is this 2 or 4 layers? You may find it's better to keep solid copper (GND most likely) on the back side, to spread out what heat conducts through the board (not all that much, really), to keep stray inductance low, than to saw it up for thermal pads (which really don't have anywhere to go, among the 4-5 nets with heatsinking implied by your via use). Especially if it's switching 5A.
Whereas if it's 4 layers, you can put whatever you want on the bottom side, and have ground on the inner top layer (assuming this is a top layer view), much closer to the footprint (less board thickness to conduct heat through), which does a quite good job indeed.
You can also get better thermal performance using a thinner 2-layer board, but less than 0.8mm thickness is likely custom, and even then they usually charge a little more for 0.8 versus 1mm. Whereas the outer layer to inner plane distance in a 4-layer board is typically 0.2mm or thereabouts (see mfg layer stackup).
Hm, I don't see an inductor (unless the big thing on the right is), is it actually just a battery management switch (over/under charge), not a regulator? You didn't say...
Tim