But the board's chief executive has warned the extra numbers are putting NHS services under strain.
NHS Greater Glasgow and Clyde saw a 50% increase in referrals in September and October with potential symptoms of the disease.
In October alone – the month after the campaign featuring actress Elaine C Smith was launched – 1700 women in the board's area were sent for further testing – up 600 cases on the same month last year.
The bold campaign received widespread publicity and featured Smith holding a number of pictures that displayed breasts showing early signs of the disease.
Robert Calderwood, chief executive of NHS Greater Glasgow and Clyde, said greater capacity in treatment was essential to improve survival rates and back up the aims of the early detection drive.
He said: "There has been a marked take-up of women coming in and it starts to put a strain on current resources. We are looking now at radiotherapy resources to take it forward."
Mr Calderwood said the effect of the Elaine C Smith campaign could have prompted an initial rush of women but said the figures would be at the "slightly higher" end of what the health board had been expecting should they be maintained.
The overall message was that lumps are not the only symptoms of breast cancer. Mr Calderwood said greater capacity in treatment was essential to improve survival rates and back up the aims of the early detection drive.
"October was the first month after the national ad campaign with Elaine C Smith and it is also breast cancer month. If it were to maintain (the figures) at that level, it is in the slightly higher range of what we would expect. It is a challenge.
"You have 580 more women in one month to be screened timeously and that is an increased demand on capacity.
"Radiotherapy capacity in west Scotland needs expanding before going forward.
"We have 11 radiotherapy accelerators that are almost at full capacity and if we are to have this year-on-year increase for demand we have to get additional capacity in the next two to three years."
The early detection campaign is due to cover the three most common cancer killers in Scotland; the focus first on breast cancer and then on bowel and lung cancer.
Health boards across Scotland will be expected to achieve a 25% increase in those diagnosed and treated in the first stages of the three types of cancer combined by 2015.
The campaign is costing the Scottish Government £30million, with extra money to be paid to health boards to increase early detection rates.
It is understood £12m-£14m will be shared out on an annual basis from next year.
Mr Calderwood added: "I don't know if it is enough to deal with the extra demand, but it is significant new money."