No. St. Norbert had other options.
In the extraordinary form of the Latin liturgy, a document titled De Defectibus in Celebratione Missarum Occurrentibus (On Defects Occurring in the Celebration of Masses) addresses such situations. According to it,
If before the Consecration a fly or spider or anything else falls into the chalice, the priest is to pour out the wine in a suitable place, put other wine into the chalice, add a little water, offer it, as above, and continue the Mass. If after the Consecration a fly or something of the kind falls into the chalice, he is to take it out, wash it with wine, burn it after the Mass is over, and throw the ashes and the wine which was used for washing into the sacrarium. (10.5)
That St. Norbert preferred to risk death than take the chance of profaning the Eucharist was a heroic virtue, but protecting the Eucharist did not require him to consume the spider.