From your description it seems to make perfect sense: not only you may calculate the mean ROC curve, but also the variance around it to build confidence intervals. It should give you the idea of how stable your model is.
For example, like this:

Here I put individual ROC curves as well as the mean curve and the confidence intervals. There are areas where curves agree, so we have less variance, and there are areas where they disagree.
For repeated CV you can just repeat it multiple times and get the total average across all individual folds:

It's quite similar to the previous picture, but gives more stable (i.e. reliable) estimates of the mean and variance.
Here's the code to get the plot:
import matplotlib.pyplot as plt
import numpy as np
from sklearn.datasets import make_classification
from sklearn.cross_validation import KFold
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import roc_curve
X, y = make_classification(n_samples=500, random_state=100, flip_y=0.3)
kf = KFold(n=len(y), n_folds=10)
tprs = []
base_fpr = np.linspace(0, 1, 101)
plt.figure(figsize=(5, 5))
plt.axes().set_aspect('equal', 'datalim')
for i, (train, test) in enumerate(kf):
model = LogisticRegression().fit(X[train], y[train])
y_score = model.predict_proba(X[test])
fpr, tpr, _ = roc_curve(y[test], y_score[:, 1])
plt.plot(fpr, tpr, 'b', alpha=0.15)
tpr = np.interp(base_fpr, fpr, tpr)
tpr[0] = 0.0
tprs.append(tpr)
tprs = np.array(tprs)
mean_tprs = tprs.mean(axis=0)
std = tprs.std(axis=0)
tprs_upper = np.minimum(mean_tprs + std, 1)
tprs_lower = mean_tprs - std
plt.plot(base_fpr, mean_tprs, 'b')
plt.fill_between(base_fpr, tprs_lower, tprs_upper, color='grey', alpha=0.3)
plt.plot([0, 1], [0, 1],'r--')
plt.xlim([-0.01, 1.01])
plt.ylim([-0.01, 1.01])
plt.ylabel('True Positive Rate')
plt.xlabel('False Positive Rate')
plt.show()
For repeated CV:
idx = np.arange(0, len(y))
for j in np.random.randint(0, high=10000, size=10):
np.random.shuffle(idx)
kf = KFold(n=len(y), n_folds=10, random_state=j)
for i, (train, test) in enumerate(kf):
model = LogisticRegression().fit(X[idx][train], y[idx][train])
y_score = model.predict_proba(X[idx][test])
fpr, tpr, _ = roc_curve(y[idx][test], y_score[:, 1])
plt.plot(fpr, tpr, 'b', alpha=0.05)
tpr = interp(base_fpr, fpr, tpr)
tpr[0] = 0.0
tprs.append(tpr)
Source of inspiration: http://scikit-learn.org/stable/auto_examples/model_selection/plot_roc_crossval.html