Would marine algae be able to live below 100 meters with only chlorophyll a?

Probably yes.

Explanation:

Lets check some facts:

1) Chlorophyll a absorbs 2 wavelengths best: 430nm (blue) and 662nm (red) (see first figure)

2) Sea water absorbs some wavelengths of color spectrum as it gets deeper. A diver can experience this in first hand with the absence of colors. Red and violet is the first two that is cannot be seen anymore (see second figure) . But blue light can reach up to 200 meters but there is a catch: with higher turbidity this can be reduced. So; since chlorophyll a can absorb blue light marine algae can survive with only chlorophyll a up to 200 meters in oceans (see third figure).