Yes, there is no contraindication for not having sexual intercourse after an artificial insemination (AI), as long as it has been performed with a spontaneous cycle.
However, if the AI has been performed with a stimulated cycle, some differences should be established in terms of partner sperm or donor sperm.
An artificial insemination with partner sperm is performed by adjusting the schedule after ovulation induction to perform it once only after adequate prior abstinence, at the exact time and in a single attempt. Subsequent intercourse is not contraindicated as long as there is no ovarian hyperstimulation that would contraindicate intercourse.
In an artificial insemination with ovarian stimulation with donor sperm, we have frozen sperm and we can program it to perform one or more inseminations in the same cycle. There is no need for prior abstinence and sexual intercourse is permitted at any time before or after insemination.
In short, what limits sexual relations is not AI, but the availability of the partner's sperm in the case of conjugal artificial insemination, since we need to have the partner's sperm available for the moment the procedure is to be performed. However, when donor sperm is available, it will be available at any time. The limitation in the relations will be determined by the ovarian stimulation and the need for rest that it requires.