Yes. You would expect to get efficiency gains.
Efficiency-design capabilities of designers of new and old equipment and Cost / efficiency manufacturing tradeoffs which have been made will have significant impact on what you can achieve. (Efficiency of "what the market will accept" and "best we can do" implementations varies substantially..
Whether it's worthwhile depends on cost versus other options.
To go 12VDC - 110 VAC - PSU/+12/+5/...
Requires energy losses in the upconversion to AC - probably in the 10% to 20% losses range depending on how hard you try. Probably not less than 5% no matter how hard you try.
Making 5/12/... from 110 VAC or 12 VDC will incur losses however done.
110 VAC supply should do this with 5% to 20% losses BUT that's an estimate - I've not measured a typical PC supply to see. Easily enough done.
Making 5/12/... also requires a switching power supply.
12 -> 12 is lossless IF battery version of 12V is acceptable. As battery can droop to 10 - 11 V it MAY need boosting and as it cab go over 12 V you may need buck boost. Say 5 - 15% losses range. 5% only with great care.
12 -> 5VDC requires a standard buck converter. Say 10% losses.
Other voltages say 3.3V and CPU voltages of 1.XV.
Say 10 -15 %. Could be 5% with great care.
So overall estimates:
Difference is perhaps break even (80/80) to as good as 90/70 =~ 30% improvement.
Liable to be somewhere in between - say a 15% to 25% gain.
This translates directly either into increased run time or reduced PV panel capacity if solar powered. Or greater safety factor.
If you do this in a solar powered system then also using an MPPT PV panel controller would make great sense.