As a drone hobbyist, is flying below the listed FAA UAS ceiling a violation of controlled airspace?
As of now, since the LAANC pre-authorization system is not yet up and running for recreational SUA flyers, any recreational sUAS operation below 9000' MSL in the lower left corner of the grid square highlighted in the question would be violating the applicable rules. In the rest of the grid square highlighted in the question, recreational sUAS operation from the surface up to 400' AGL violates no rules.
Now read on for more:
In the particular grid square that is highlighted in the question, the LAANC pre-authorization system will only authorize a ceiling of 100'. But the questioner is mistaken to believe that the floor of the Class B airspace is 100' anywhere in that grid square.
The lower left corner of the grid square highlighted in the question has Class B airspace extending from the surface upwards. In that airspace, a recreational sUA flyer can not legally fly a drone without prior authorization. Since the LAANC pre-authorization system is not even operational yet for recreational sUA flyers, to legally fly in any airspace that is Class B at the surface, a rec SUA flyer would have to fly at a "blue dot" fixed site. "Blue dot" fixed sites are typically prescribed the same ceiling as the ceiling specified for the LAANC grid square in which they are located, which in this case would be 100 feet. No "blue dot" fixed site currently exists anywhere in the Class-B-to-surface airspace around Phoenix.
Once the LAANC pre-authorization system is up and running for recreation sUA flyers, a rec SUA flyer will be able to use that system to get pre-authorization to fly from the surface up to 100' AGL anywhere in the grid square highlighted in the question.
But does this mean a recreational sUA flyer is limited to a ceiling of 100' AGL if he or she is flying in a part of the grid square highlighted in the question that does NOT have Class B airspace at the surface?
No it does not.
And does the fact that LAANC pre-authorization is not yet available to recreational SUA flyers have any impact on recreational sUA flight in any point within a LAANC grid square if the airspace at that particular point, from the surface up to 400', is NOT Class B, Class C, Class D, Class E airspace that extends down to the surface and is "designated for an airport", or some other kind of restriction such as those shown by the heavy red markings on the LAANC map?
No it does not.
In all but the lower-left corner of the grid square highlighted in the question, the Class B airspace has a floor of 5000' MSL. Below that is Class E (E5) airspace down to 700' AGL and Class G airspace from 700' AGL down to the surface. In that airspace, one can legally fly a drone (sUA) up to 400' AGL with no prior authorization of any kind, either as recreational flyer or as a non-recreational flyer, despite being in a LAANC grid square.
VFR sectional chart view, centered on Phoenix: http://vfrmap.com/?type=vfrc&lat=33.434&lon=-112.012&zoom=10
However, if a rec SUA flyer doesn't fully understand the airspace system or how to read a VFR sectional chart, he or she would be wise to stay on the safe side and avoid any operations within any LAANC grid square until the LAANC pre-authorization system becomes operational for sUA flyers, unless he or she is flying at a "blue dot" fixed site.
The phrase "within the lateral boundaries of the surface area of Class E airspace designated for an airport" refers to Class E airspace that extends down ALL THE WAY DOWN TO THE SURFACE. More specifically, it refers to E2 airspace, but not E3/E3a/E4 airspace. To read more about this, visit this outside link to a forum for rc flyers-- "Understanding E4 airspace-- prior authorization not required".
No Class E airspace is present at the surface anywhere in the region depicted in the illustration accompanying the question.