When the GPS downgrades the approach to LNAV, no, repeat no, vertical guidance is provided. The pilot is expected to fly the approach according to the published LNAV procedure and MDA. The GPS does not compute a glidepath, period, so following an LNAV/VNAV to a DA is not supported. GPS WAAS does not have Baro VNAV equipment but is authorized to fly LNAV/VNAV approaches using the GPS WAAS equipment, providing the GPS signal meets the criteria for integrity. Baro VNAV is a totally different piece of equipment and the odds of you having it in your aircraft are very close to zero. My understanding is that this equipment often can cost in the hundreds of thousands of dollars.
The WAAS GPS doesn't know or care what minimums you fly to. It only tells you what the highest in the hierarchy of minimums (LPV, LNAV/VNAV, LNAV+V, LNAV)you are authorized to fly and that it will provide guidance for. It is the responsibility of the pilot to follow the rules.
Since you don't have a Baro VNAV system, it is not legal to fly to LNAV/VNAV minimums if the WAAS GPS downgrades to LNAV. As a side note, often the LNAV/VNAV minimums are higher than the LNAV minimums, particularly with respect to visibility, but often the DA is higher than the MDA. The whole purpose for LNAV/VNAV minimums was to provide for a stabilized approach for the airlines even if it meant a reduction in minimums.
Some more information:
When you load the approach into the WAAS GPS, it will identify one and only one of the following in the hierarchy of minimums: LPV, LNAV/VNAV, LNAV+V, or LNAV. LNAV+V wont show up as a minimum choice on the approach plate as it is only an LNAV minimum approach with an advisory glidepath. Any particular approach may offer more than one in the list above, but only the first in the hierarchy is listed in the database. The GPS doesn't care what minimums you fly an approach to, that is totally the pilot's choice. Just because an approach has vertical guidance available, doesn't mean you need to use it if LNAV minimums are available for the approach and you choose to fly the approach to the LNAV minimums.
One minute prior to the final approach fix, the WAAS GPS will determine if the GPS integrity is sufficient to support vertical and horizontal guidance on the approach of the highest in the hierarchy of minimums. If it fails this check, the approach is downgraded to LNAV minimums and no vertical guidance is provided. So if the approach has LPV minimums as the highest in the hierarchy, it will downgrade to LNAV minimums, even if the approach also supports LNAV/VNAV or LNAV/+V. If a particular approach has LNAV/VNAV as the highest, it still downgrades to LNAV. In very rare cases, the integrity is bad enough that even LNAV horizontal integrity isn't satisfied, in which case you are waived off by the GPS. In some other cases, there are stand alone LPV approaches that do not have an associated LNAV procedure, and if the integrity doesn't meet the criteria for the approach, you are waived off as well, since there is no LNAV minimums to downgrade to.