MSP430FR2355: ADC channel setting problem

Short answer: No. An ADC sequence always counts INCH -> A0. [Ref User Guide (SLAU445I) Sec 21.2.7.2]

With digital pin usage, the small sips of current taken by the sample/hold circuit aren't normally enough to disturb anything. I don't know if this can be said for opamp (analog) signals.

Taking a step back: Since the FR2355 has no DMA, and the samples in the sequence (with MSC=1) are typically arriving very fast, it is problematic to collect one before the next arrives; if you get out of sequence (overrun) it's somewhere between difficult and impossible to detect it. One solution is to slow the ADC down (slow clock or very long S/H) but this takes extra time and doesn't truly avoid the race.

Particularly since you're only interested in half of the results, it might be quicker (less delay between samples) to just do two conversions (A3 and A0) using CONSEQ=0 and a spin loop. That would avoid the race and avoid poking at your opamp channels.