If you wish to analyse the result statistically, then no. There is just as likely to be variation in your control plots as there is in any treatment, so for any stats you'll need your control replicated as much as for your treatments.

Having said that, in the real world we don't always need to analyse everything statistically, and often have limited resources. It depends exactly what you are looking at and what you intend to do with the result. If all your treatments are things that you know already will make a large difference from the control, your real question is simply which treatment is better, and the control is simply being measured to give a rough value to compare against for discussion or demonstration purposes, then you might be able to get away with no replication on it. You'd need to be very clear from the start that you will never be able to analyse this part of the result statistically, all stats will be done between treatments only. If this is a problem, you need to replicate the control.

If you have access to a statistician, it is good practice to run all trial designs before them before starting, to check that you'll be able to do all the analysis you need to at the end.

I think you should follow split split plot with RCBD...all plots should be of equal sizes

Thank you Sir