No! While symptoms may be mild or nonexistent at onset, the existence of antibodies may be a contributor to a whole host of psychological and nervous conditions.
Authors of an article titled Latent Toxoplasmosis and Humans (retrieved from the National Institute of Health database) review 42 studies of latent toxoplasmosis (asymptomatic), which established links between toxoplasmosis antibodies and "schizophrenia and depressive disorders, obsessive–compulsive disorder, Alzheimer's diseases and Parkinson's disease, epilepsy, headache and or migraine, mental retardation and intelligence quotients..."
And this is from the abstract of another such article (Influence of latent Toxoplasma infection on human personality, physiology and morphology: pros and cons of the Toxoplasma-human model in studying the manipulation hypothesis):
The parasitic protozoan Toxoplasma gondii infects about one-third of
the population of developed countries. The life-long presence of
dormant stages of this parasite in the brain and muscular tissues of
infected humans is usually considered asymptomatic from the clinical
point of view. In the past 20 years, research performed mostly on
military personnel, university students, pregnant women and blood
donors has shown that this 'asymptomatic' disease has a large
influence on various aspects of human life. Toxoplasma-infected
subjects differ from uninfected controls in the personality profile
estimated with two versions of Cattell's 16PF, Cloninger's TCI and Big
Five questionnaires. Most of these differences increase with the
length of time since the onset of infection, suggesting that
Toxoplasma influences human personality rather than human personality
influencing the probability of infection. Toxoplasmosis increases the
reaction time of infected subjects, which can explain the increased
probability of traffic accidents in infected subjects reported in
three retrospective and one very large prospective case-control study.
Latent toxoplasmosis is associated with immunosuppression, which might
explain the increased probability of giving birth to a boy in
Toxoplasma-infected women and also the extremely high prevalence of
toxoplasmosis in mothers of children with Down syndrome.
Toxoplasma-infected male students are about 3 cm taller than
Toxoplasma-free subjects and their faces are rated by women as more
masculine and dominant. These differences may be caused by an
increased concentration of testosterone. Toxoplasma also appears to be
involved in the initiation of more severe forms of schizophrenia. At
least 40 studies confirmed an increased prevalence of toxoplasmosis
among schizophrenic patients. Toxoplasma-infected schizophrenic
patients differ from Toxoplasma-free schizophrenic patients by brain
anatomy and by a higher intensity of the positive symptoms of the
disease. Finally, five independent studies performed in blood donors,
pregnant women and military personnel showed that RhD blood group
positivity, especially in RhD heterozygotes, protects infected
subjects against various effects of latent toxoplasmosis, such as the
prolongation of reaction times, an increased risk of traffic accidents
and excessive pregnancy weight gain. The modern human is not a natural
host of Toxoplasma. Therefore, it can only be speculated which of the
observed effects of latent toxoplasmosis are the result of the
manipulation activity of the Toxoplasma aimed to increase the
probability of its transmission from a natural intermediate to the
definitive host by predation, and which are just side effects of
chronic infection.