Am I entitled to automatically become an indeterminate employee after three years of continuous employment provided there is no interruption of continuous service?

It depends.  Term employees employed in the same department for a period of three (3) continuous years (without a break of 60 consecutive calendar days or more) must be appointed as an indeterminate employee at the level of his/her substantive position.  Having said this, there may be certain exceptions, where the source of funding for salary dollars is from external sources and for a limited duration (sunset funding) or where the department puts a hold on ongoing accumulation of service for the purposes of conversion to indeterminate status where it can be established that the indeterminate appointment of term employees would result in workforce adjustment situations.  For more information on this, see section 7.2 of the Term Employment Policy.

Notice:

The Department of Justice and Public Prosecution Service of Canada have exercised their right to suspend the ongoing accumulation of service under the Term Employment Policy for the purposes of conversion to indeterminate status. The decision is effective May 8, 2012 at DOJ and June 1, 2012 at PPSC. The two departments have advised the AJC that service for term employees will not count as continuous for the purposes of conversion to indeterminate status, until further notice.

This means that the accumulation of service for term employees who did not reach 3 years of continuous service before May 8th, 2012 (at DOJ) and June 1, 2012 (at PPSC) will cease on these respective dates.