Every since AC97 became a thing, most sound cards no longer have any hardware based support for 44KHz sample rates. Things rely on software (pretty much best option) or hardware (usually subpar) to do the resampling. There's also the question of what happens when multiple sound streams are playing, hardware usually can only play back one stream and even if there's support for more you get hardware based resampling from an arbitary rate to 48KHz for the final mix and result is often not that good.
Cards that can definitely do either natively have two crystals, one is typically 24.576000MHz for 6/12/24/48/96/192KHz and other is 16.934400/22.579200/33.868800MHz for 5.5/11/22/44/88/172KHz. PLL options also exist from what I have seen it isn't all that common and I don't have any hardware that uses such a method.
Some single crystal things can do 44KHz by utilising a divider that results in something near 44100Hz from 48KHz based clock but this has a huge drawback that there are no longer 256/384/512 cycles per sample and the oversampling filters in the DACs and ADCs really really really don't work properly anymore and you get excess artifacts still. There are some AC97 things that do it and I have seen it in HDAUDIO codec datasheets too. Rates being slightly off is not a problem, unless they're very off (several % rather than 0.0something%) you aren't gonna hear anything. PLL methods aren't going to give exact rates either but they will not have the problem of differing cycles per sample from the DAC/ADC.
The sound quality slider in Windows will not have any effect on hardware based resampling from my experience, only software mixing and does make a dramatic difference.
If you really want uncomditional best possible output from 48KHz based thing (AC97, vast majority of PCI(-E) sound cards and most/all USB sound cards) you'll use a nice media player such as XMplay and make it output 48KHz (or a multiple) on all formats unless you're absolutely sure the hardware has real support for 44KHz and driver isn't going to do any unnecessary resampling. For windows Vista+ you can choose what all sources get resampled to (in software) in the audio control panel and there end your troubles when you choose the native rate of the hardware. Hardware acceleration in games doesn't exist either anymore from what I know so you do get consistent results regardless of hardware if that setting is chosen right.
On my ESI Juli@ control panel you can see what clock the driver chooses in automatic mode and driver there resamples everything to 44KHz for all non standard rates. On my Yamaha DS2416 I can choose the internal sample rate which can vary from 40 to 50KHz, all sources are then treated at that rate with hardware based resampling which isn't the cleanest there is even though the card is a pro piece of great and my Yamaha SW1000XG is completely locked to 44KHz with no option to chance the rates. Hardware does resampling there too with WDM drivers and you get same sort of artifacts as most other hardware gives and result isn't all that great. With WDM drivers hardware mixing is no longer used and if sound quality slider is set to max in the control panel you get distortionless output. Creative cards (Live and newer) have given me pretty much same results though there seem to be excess artifacts on the spectrograms in ultrasonic range even if you feed 48KHz to them. Yamaha 71x cards (ISA) have support for 44 and 48KHz and the VXD driver chooses right one as needed and throws MMSYSTEM error on unsupported rates, windows sound quality slider has no effect there either. YMF7xx PCI cards don't have any 44KHz support whatsoever similar to Creative cards, resampler is not all that great either but there seem to be some workarounds with some driver versions that produce acceptable results.
For games you're out of luck, all older stuff is 44KHz based while newer stuff is 48KHz based and you'll not have any control over how their sound gets output for the most part. Cards supporting both 44 and 48 don't support things like EAX and A3D but games using those should also use 48 so there shouldn't be problems but I haven't looked at games in detail, only general sound/music stuff.