Dependent variable plays the role in selecting regression not independent variable,
it means that because your dependent variable is binary so you must use logistic regression.
please read the below explanations from SPSS help about logistic regression and ordinal regression:
Logistic regression is useful for situations in which you want to be able to predict the presence or absence of a characteristic or outcome based on values of a set of predictor variables.
Ordinal Regression allows you to model the dependence of a polytomous ordinal response on a set of predictors, which can be factors or covariates.
So you will lose some information and your accuracy in using Logistic regression instead of Ordinal Regression and its wrong to use Ordinal Regression instead of Logistic regression because your response in logistic regression is as nominal variable not ordinal.