It wouldn't have happened. Elizabeth basically had the following view on marriage:
1. While the ministers wanted her to marry, she herself was somewhat dissuaded by her personal experiences of the marriages of her father and her half-sister.
2. That in any case by not marrying she remains in full control of the reigns of power, and can continue to move between factions rather than being tied to any one of them.
3. That marriage could create the situation of the 'Second Person' who, much like herself in the reign of Mary I, or Mary Queen of Scots to her, would become a magnet for plots and rebellions.
4. That the only possible choices were a foreign prince, or an English noble. In the former, the reign of Mary I had proven that the English people were distrustfull of foreign Princes in general, and Catholic ones in particular (thus ruling out d'Alencon), and in the latter the result would be to raise one man above his stature, favouring one faction and creating division and disloyalty in the court.
5. That remaining unmarried she could also project the image of being 'married to England', effectively creating a populist myth around her.