Currently reverve combat troops are doing more than their annual month of service due to the intifada.
In time of all-out war with full mobilization over 500,000 reserves can join the standing army in about 48 hours and ready to roll on 3 fronts.
Yes, they have a draft, a universal one, with some exeptions, mainly religious objections. They also draft both sexes, but IIRC married women don't get drafted. About 1/5 of men and 1/4 of women do not serve for various reasons.(about 1/2 of the men for religious reasons, the others for medical reasons, or such reasons as being out of the country) Draft is, I think, 18 for both sexes, any event most enter the army (technically the IDF)
Men serve in the IDF for three years, women for one year and nine months, but that's only active service, reserve service is much longer. Officers have served as enlisted draftees before becoming officers. They've called up signifigent numbers of reserves in the last year plus, but then so have we.