The answer is not necessarily.
In a constraint budget, you may be forced to lower your keyword bids, however, as a result of this, it is not unusual to see more clicks and higher conversions at lower cost per conversion.
When you lower your bids, if you’ve optimised your keywords and your budget remains constant, you are likely to get more qualified clicks.
More qualified clicks means more conversions and a higher conversion rate.
A higher number of conversions coupled with a higher conversion rate means a lower cost per conversion.
Extract from my Book ‘Making Google Ads Work’.