I have a dataset containing images, each image has a single cell along with some smaller inconsequential cells in the background. Can this dataset be used to train a model to detect and recognize multiple target cells in a single test image?
Secondly will having a different size of cell in the training data to the size of cells in the test image affect the prediction?
This sounds like a multi object detection (MOD) problem. You will need to train a MOD-model such as YOLO or SSD with your images (required format and procedure varies by framework and network architecture), then they should be able to detect multiple instances of the data they were trained on. Whether you train with images containing only one instance or several instances should not make a fundamental difference. Note that the training and inference processes are not easy tasks, however, if you don't have a solid background in neural networks and some programming language (e.g. Python).
I would recommend looking for some blog or youtube tutorials on customized multi object detection and following those.
