Someone can, yes, and no particular amount is required.
All antidepressants can involve overdose, and there is nothing strictly defining what “overdose” means because all outcomes that can be caused by overdosing can also be caused by normal dosing. “Overdose” most conventionally just means “more than you were prescribed”, in this case, because all doses of Zoloft and other antidepressants are toxic and all doses can involve serious, disabling, lasting, or fatal side effects. Furthermore, no doses are more clinically effective for alleviating depression (or anxiety) than placebo.
Though all doses of antidepressants are risky and potentially deadly, different classes of antidepressants (like SSRIs and TCAs, etc) have different likelihoods of particular side effects, including differences in overdosing effects. The likelihood of particular reactions also changes between the individual drugs within a class, though all antidepressants of any type cause brain dysfunction, systemic dysfunction, and withdrawal syndrome.
The severity of side effects associated with overdoses is not consistent between patients, even on the same drugs or in similar dosages of overdose. Just like the effects of normal dosing, how intensely or problematically someone reacts to taking excessive amounts of Zoloft cannot be predicted. There is no hard dosage line between serious, moderate, or mild overdose experiences, and there is no dose that is guaranteed to be safe or guaranteed to kill you.
For an example of the observed survivable extremes, a 1996 study into 40 sertraline overdoses reported to poison control saw people taking amounts of up to 8,000mg (which is 40 times the maximum clinical dose for sertraline). The median dose was 1,400mg, so most patients were taking overdoses into the thousands of milligrams. Nobody from these reports died of overdose, and some were considered by emergency room staff to be completely asymptomatic.
Many dangerous or potentially disabling side effects of antidepressants, including SSRIs like sertraline, can be impossible to see through basic examination and are not tested for (or unable to be tested for) in most patients, so one could not characterize these reactions as inherently minor or limited.
Combining sertraline with other drugs (prescription or otherwise) was associated with a higher rate of notable overdose effects, as one would expect with psychotropic drugs, but serious overdose effects are sometimes seen in patients only taking sertraline. Many patients were treated and released in a matter of hours or days, and there was no information gathered about the long term outcomes of these overdoses.
You can read that study here: Sertraline overdose.
In another journal article drawing from multiple sources talking about of overdoses on sertraline, reports of overdose effects were seen with doses as low as 200mg (which is still within the prescribed range of doses, so this was in someone prescribed less, or a non-patient). Serious acute side effects were seen in overdoses as low as 500mg, and death in doses as low as 1,100mg, though how much of a role the sertraline alone played may vary from case to case.
You can read that article here: http://www.tandfonline.com/doi/pdf/10.1080/15563650701285289
If you are asking about fatal overdoses specifically, overdosing on antidepressants as a method of suicide or accidental death is not usually as fatal as methods using more commonly deadly drugs, but it is still quite possible to die from both normal doses and overdoses. Reuptake inhibitor antidepressants that have multiple primary neurotransmitter targets–like SNRIs, Tricyclics, and NDRIs–often have a more volatile impact than ones with single primary targets, like SSRIs. All antidepressants impact multiple receptortypes, however, and Zoloft can produce side effects and overdose problems related to more than just serotonin receptors.
Mixing antidepressants with other psychotropic substances can greatly increase the danger of death, and is more of a predictor than the dosage of antidepressant taken. MAOIs and some of the other classes have more prominent interactions with foods and other substances than reuptake inhibition antidepressants, so normal foods and drinks can also contribute to overdoses and toxic damages with some drugs, especially inadvertent ones. These interactions can be due to how a drug is metabolized, circulated, or acting on particular systems.
If you are concerned about a particular individual or situation, please call 911, your local emergency room, or poison control immediately! Antidepressants are neither a painless nor a reliable way to harm or kill ones self, and seeking immediate help for any desires to commit violence against self or others is essential.
Here are two other Quora posts I have written on this topic. The first examines the details of overdose in SSRI antidepressants, which includes Zoloft (sertraline). The second deals with fatal outcomes of antidepressant use, including purposeful and accidental overdoses.