Suicide threats were considered a severe mental health issue and yes could legally allow for an abortion per the physician's discretion as being necessary to preserve the life of the mother. This was especially true if the woman already had a mental illness pre-pregnancy and required treatment that could be injurous to a developing fetus. However, physicians were usually required by hospital policy to bring the case before a committee to determine whether the proposed abortion was appropriate to the woman's health needs. Some of these committees often coercively required the woman to be sterilized after the abortion before they would sign off on the case. But considering how several physicians, including psychiatrists, must be in agreement for the procedure to happen, you can imagine how very rarely abortions were performed due to mental illness...
Mental health issues like suicidal tendancies are even still today considered medically serious enough to warrant or justify a later abortion (pre-viability) or termination of the pregnancy. But a viable, healthy fetus though would most likely be delivered early via labor induction for two reasons. One, once the pregnancy is past about 26 weeks, any abortion attempts would present similar level risk factors to childbirth and therefore would be ruled out as a health threat to the woman (esp. regarding future fertillity). Two, by 26 weeks, a developmentally normal fetus is likely going to be viable and capable of surviving outside the womb and per the Casey decision, the state can intervene or regulate when a viable fetus can be protected and expected to be delivered live.
I post this link occassionally but if you have some time to spare and are interested in a radio documentary on the pre-Roe days, go to
http://www.albany.edu/history/FromTheBackAlleys.html . This issue is mentioned and explored as part of this documentary.