No, flu viruses or coronaviruses will not lay dormant in one's body. Some viruses, like HIV, that insert their DNA into the cells they infect, however, can lay dormant in the body and reactivate at a later time.
COVID-19 has the possibility of becoming quite widespread as it seems to be easily transmitted person-to-person, people have no pre-existing immunity, and no vaccine is available. Current observations suggest that while the vast majority (~80%) of those infected experience only mild symptoms, about 15% require hospitalization and about 2% could die from the disease. These numbers for hospitalizations and mortality are higher than for the typical seasonal flu, and could strain the healthcare resources of even developed nations if faced with outbreaks like those seen in Hubei province.
However, it is worth noting that we have been able to contain outbreaks of viruses that are similarly contagious as COVID-19 (e. g. the
2003 SARS outbreak in China, which was caused by a similar coronavirus), so well executed public health efforts to quarantine the infected and trace contacts can be effective in stopping the spread of the virus.