Die GT1030 ist zu breit und kann nicht in einen SFF eingesetzt werden!! Maximale Breite ist 2.1 cm., also z.Z. nur HP AMD Radeon RX550X (HP 5LH79AA), die gem. Spezifikationen kompatibel ist und auch eine Auflösung von 5120x2880 @ 60 Hz hat.
That is an interesting question. In terms of hardware it seems that the motherboard can support it. In fact it has a PCI express x16 (v 3.0) slot, and it can support 2.5' in full height, 6.6' in length and 35W max. power. This is good, as the power consumption of the GT1030 is at 30W.
But on the other hand, this graphics card is in fact quite bulky (3.80 cm in width), because it is passively cooled, and takes as much as space as two slots. Looking at the HP ProDesk 400 G3 SFF, the available PCI slot is at the very end, close to the power supply. Therefore:
1. The first question is whether you can actually fit the graphic card in the case in terms of its width. 2. The second question is whether being so close to the PSU unit while being passively cooled is a good idea in terms of performance.
I would recommend that you open the case, and measure the space you have available. If there is a sufficient space, and the flow of air in the case is not terrible, maybe it makes sense to give it a go on the GT1030.