No, people just count いち、に、さん、し、ご、ろく、しち...

There is, however, a tendancy to say し over よん and しち over なな when excercizing.  Especially when exercizes are counted in small groups (often I hear my students saying 1-2-3-4 or 1-2-3-4-5-6-7-8 over and over again when exercizing together during practice, always with し and しち).