No, because「星」was not the original character for the word meaning star.
「星」was originally written「晶」:
These are oracle bone script samples, and by that stage stars were already characterised as being more numerous and smaller than the sun and moon, hence the appearance.「晶」now means sparkling/crystal/radiant, and this is a semantic extension from the original meaning twinkling stars.
Later on, a sound hint「生」was added (note, the common On'yomi for both「星」and「生」, which are both しょう and せい, are identical).
The number of stars depicted ranged from 2-5, but eventually settled on to 3:
The right hand side is the modern representation of the form on the left.
A Warring States innovation simplified it to one star,
and this is what we're left with today.
To clarify, there was a clear recognition that「星」and「日」were both celestial bodies shining in the sky, as seen by the structural composition of「晶」, but「星」is also the same term given to planets and comets, and the philosophical/cultural/religious significance of the sun itself, seen in words like「太陽」(literally Grand Yang, by far the more pervasive word for sun in Chinese), is not accorded to「星」.