Is it possible to use grayscale images to existing model?
It depends on the model. You'll have to dig into the model definition and see. 

It's not uncommon for models to grayscale images in pre-processing. In that case, you will be fine. 

However, many recent deep convolutional models operate on RGB images as 3D tensors (4D with the batch dimension). In this case, you should consider modifying the model so that it operates on a single color channel before training it. Multi-channel convolution is discussed in the convent's chapter of Goodfellow's Deep Learning.