No, the vertical component of LPV approach performance is based on WAAS GPS input, not the altimeter or barometric system.
Your assumption about LPV performance is correct: Baro-VNAV is not used for LPV approaches.
On any type of approach with a Decision Altitude (DA), the aircraft's arrival at the DA is determined by the pilot's reading of the aircraft's sensitive altimeter.
If the altimeter is set to an altimeter setting report from a distant reporting station, SFO in this case, then the DA may be increased to give additional altitude margin to allow for variance in local atmospheric pressure.
This is true for the DA or Minimum Descent Altitude (MDA) on any approach, whether a GPS approach or not. See the MKT ILS 33 and MKT RNAV 15 for other examples of this. See the following excerpts from the Aeronautical Information Manual on altimeter settings for approaches (emphasis mine):
4. Approach minimums are based on the local
altimeter setting for that airport, unless annotated
otherwise; e.g., Oklahoma City/Will Rogers World
approaches are based on having a Will Rogers World
altimeter setting. When a different altimeter source is
required, or more than one source is authorized, it will
be annotated on the approach chart; e.g., use Sidney
altimeter setting, if not received, use Scottsbluff
altimeter setting. Approach minimums may be raised
when a nonlocal altimeter source is authorized. When
more than one altimeter source is authorized, and the
minima are different, they will be shown by separate
lines in the approach minima box or a note; e.g., use
Manhattan altimeter setting; when not available use
Salina altimeter setting and increase all MDAs
40 feet. When the altimeter must be obtained from a
source other than air traffic a note will indicate the
source; e.g., Obtain local altimeter setting on CTAF.
When the altimeter setting(s) on which the approach
is based is not available, the approach is not
authorized. Baro−VNAV must be flown using the
local altimeter setting only. Where no local altimeter
is available, the LNAV/VNAV line will still be
published for use by WAAS receivers with a note that
Baro−VNAV is not authorized. When a local and at
least one other altimeter setting source is authorized
and the local altimeter is not available Baro−VNAV
is not authorized; however, the LNAV/VNAV
minima can still be used by WAAS receivers using the
alternate altimeter setting source.
Note that Baro-VNAV is a type of VNAV system which uses barometric
altimetry as a basis for vertical navigation performance. An LNAV/VNAV approach can be flown using WAAS equipment without a Baro-VNAV system.