Valid use of repeated measures ANCOVA?

I am running a repeated measures study with four time points. A single group of participants receive the same questionnaire at each time point, which is assessing variable X. I am determining how variable X changes over time. I plan to analyze this in SPSS using a repeated measures ANOVA (with follow-up tests).

Participants are also filling out an additional questionnaire at the beginning of the study (one assessment only). This questionnaire is assessing a continuous variable, which I will call variable Y. I want to see if changes in variable X vary according to variable Y. For instance, perhaps participants scoring higher on variable Y show little or no change in variable X over the four time points, whereas those scoring lower on variable Y steadily increase on variable X over the four time points.

My original plan was to analyze this using a repeated measures ANCOVA, entering variable Y as a covariate (and variable X as the repeated measure). I would be looking at the interaction between X and Y in the output. I am wondering if anyone can tell me whether this is a valid analysis. I am questioning myself because I typically use ANCOVA to control for a covariate (i.e., the covariate is a secondary concern in the analysis); whereas in this case, I am essentially trying to use the covariate as a continuous predictor of X.

Additional details: sample size is N = 80; I am not missing any data for either variable X or Y.