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Question: Was Communism historically signified by the color RED or not?
Yes or No will suffice.

No.

The reason for this is that red has historically signified many other things, especially with different contexts:

General Symbolism
1. Courage and sacrifice
  In western countries red is a symbol of martyrs and sacrifice, particularly because of its association with blood.
2. Love
  Red is the color most commonly associated with love, followed at a great distance by pink.
3. Happiness, celebration and ceremony
  Red is the color most commonly associated with joy and well being.
4. Hatred, anger, aggression, passion, heat and war
  While red is the color most associated with love, it also the color most frequently associated with hatred, anger, aggression and war.
5. Warning and danger
  Red is the traditional color of warning and danger.
6. The color that attracts attention
  Red is the color that most attracts attention. Surveys show it is the color most frequently associated with visibility, proximity, and extroverts. It is also the color most associated with dynamism and activity.
7. Seduction, sexuality and sin
  Red by a large margin is the color most commonly associated with seduction, sexuality, eroticism and immorality, possibly because of its close connection with passion and with danger.
Red in different cultures and traditions
1. In China, red is the symbol of fire and the south. It carries a largely positive connotation, being associated with courage, loyalty, honor, success, fortune, fertility, happiness, passion, and summer. In Chinese cultural traditions, red is associated with weddings (where brides traditionally wear red dresses) and red paper is frequently used to wrap gifts of money or other objects.
2. In Japan, red is a traditional color for a heroic figure.
3. In the Indian subcontinent, red is the traditional color of bridal dresses, and is frequently represented in the media as a symbolic color for married women. The color is associated with purity, as well as with sexuality in marital relationships through its connection to heat and fertility.
4. In Central Africa, Ndembu warriors rub themselves with red paint during celebrations. Since their culture sees the color as a symbol of life and health, sick people are also painted with it.
5. The early Ottoman Turks led by the first Ottoman Sultan, Osman I, carried red banners symbolizing sovereignty, Ghazis and Sufism, until, according to legend, he saw a new red flag in his dream inlaid with a crescent.
In religion
1. In the Christianity, red is associated with the blood of Christ and the sacrifice of martyrs.
2. In Buddhism, red is one of the five colors which are said to have emanated from the Buddha when he attained enlightenment, or nirvana. It is particularly associated with the benefits of the practice of Buddhism; achievement, wisdom, virtue, fortune and dignity. It was also believed to have the power to resist evil.
3. In the Shinto religion of Japan, the gateways of temples, called torii, are traditionally painted vermilion red and black. The torii symbolizes the passage from the profane world to a sacred place. The bridges in the gardens of Japanese temples are also painted red (and usually only temple bridges are red, not bridges in ordinary gardens), since they are also passages to sacred places. Red was also considered a color which could expel evil and disease.

To associate the color exclusively with Marxism (Karl Marx: 05 May 1818 – 14 March 1883) is to ignore its history across the world... or are you trying to tell us that The Communist Manifesto (1848) and Das Kapital (1867–1894) which are less than a hundred years old can uproot and supplant thousand year old history?