Is a cross specifically used for stereocenter representation?
According to IUPAC it is not incorrect for using it to depict carbohydrates being stereogenic or not. However here is an excerpt from the link listed below:
The use of Fischer projections in non-carbohydrates is problematic. Any drawings of this type are necessarily ambiguous since it is unclear whether the author of the drawing intended to make a Fischer projection or simply happened to draw a diagram in that orientation. Molecules depicted in the style of Fischer projections are likely to be recognized as such when they contain at least two acyclic stereo- genic centers oriented vertically, although such interpretation is not guaranteed. Molecules containing a single stereogenic center pose even greater problems since it is often convenient to separate the four ligands by equal angles whether or not a single stereoisomer is intended. Accordingly, although Fischer projections of carbohydrates are acceptable, similar depictions of non-carbohydrates should be used only when the viewer of the diagram is certain to understand that the diagram was intended to represent a Fischer projection. Fischer projections should be avoided where ambiguity is possible, including when used in computer applications.
See more here (page 37-38):