Britta, it probably will survive, but it might be a few years before it flowers again. The Cymbidium experts like to have 4 maybe 5 bulbs in a division, that way the plant is not set back too much and will probably bloom next season.

Here are culture notes provided by Tinonee Orchids.

Ray’s Growing Guide - Cymbidiums

Cymbidiums are what most people first think of as orchids. This genus is easy to grow and very popular in the cooler, temperate climates of New South Wales and the southern states. Shade: These plants need shade from hot sun. A shade or bush house covered with 50% shadecloth is ideal. Alternatively, dappled shade from trees or other plants will suffice. Cymbidiums need plenty of filtered sun to flower well. These orchids will grow well, but rarely flower in full shade. If you don’t have a shadehouse it may be necessary to move the plants from more sun in winter to a shadier spot in summer. If you wish to plant cymbidiums in a garden, provide dappled shade or an easterly aspect. Never cover the roots with heavy soil or clay, rather place the plant on top of the soil and mound around it with cymbidium compost.

Temperature:

Cymbidiums will happily grow in a wide range of temperatures and will tolerate light frost as long as buds are protected. At the other end of the scale, very hot days are tolerated but plants will benefit from a substantial overnight drop in temperature. This drop in temperature will help initiate flower stems. Watering:

Cymbidiums like to stay damp but not wet. To achieve this plants may need to be watered daily during hot, dry weather. Watering in the late afternoon or evening will also help chill the plants. In winter watering weekly should suffice. Compost:

Compost needs to be well aerated and free draining, but still remain damp for a reasonable period. Most cymbidium compost available from specialist nurseries is ideal, but beware of generic brands from supermarkets. These are often of inferior quality. Graded and washed coconut husk chip such as OrchidMate is a popular media amongst orchid growers. OrchidMate is prewashed so just soak it for a few hours and it is ready to use. Treated pine bark or a perlite based mix is also popular. Repotting: Cymbidiums are best repotted during the cooler months or as soon as possible after flowering. To avoid stress to the plants avoid repotting during summer. If dividing plants make sure at least 3-4 bulbs are left together. Never reuse compost, and sterilise tools and preused pots with bleach or a sugar soap concentrate. After dividing place plants in a shady area for a few weeks and water sparingly. Fertiliser: The most effective type is water soluable fertiliser. Use a formula recommended for flowering plants. This can be applied every watering at quarter strength or at recommended strength every third watering. A little slow release fertiliser is ok but must be buried in the pot. Pests & Diseases: Red spider or spidermite is troublesome in summer, especially in warmer climates. Control these with miticide, Pest Oil or predatory mites. Scale is easily controlled by Rogor or Pest Oil. Some disease is prevalent in warm, wet weather. Black spots on leaves is easily controlled by spraying with Mancozeb or lime water. Bulb rot can be prevented by using Yates Anti Rot. Always use at the manufacturer’s recommended levels, and if in doubt seek advise from a nursery or an experienced grower.