I have worked with the coupling of SpyCatchers and SpyTags of different iterations and can confirm that they are all backward compatible. While SpyCatcher003 and SpyTag003 pairs have the quickest reaction rate, reactions of all pairs (including SpyCatcher and SpyTag version 1) should go to completion under the right conditions.
The SpyCatcher002-SpyTag1 is no exception. As you quoted in the Angewandte Chemie paper, the rate of reaction is 5.5x103 M−1 s−1. Rate = k[A][B]. This means that 10 μM of SpyCatcher002 and 10 μM SpyTag will react with a t1/2 (50% coupling) of 18 seconds at pH = 7.0. However, 10 μM of SpyCatcher002 and 10 μM SpyTag2 will t1/2 of 5 seconds (rate constant is 2x104 M−1 s−1). If you are reacting 0.1 μM of each, their respective t1/2s are about 8 and 33 minutes, respectively.
To get the reaction to go to completion (>90% coupling), you'll need to wait ~12 times as long as the t1/2 (since every subsequent t1/2 doubles in a second-order reaction). This will, of course, depend on your concentrations. However, when using low concentrations (0.1 μM), complete coupling of SpyCatcher002 to SpyTag002 will take 1.5 hours, whereas SpyCatcher002 to SpyTag will take 7 hours at 25C. SpyCatcher002 to SpyTag1 will take 3x as long to go to completion; therefore, I'd recommend using at least 1-2 μM of what you want completely coupled with an equal or 2-4x excess amount of either Tag or Catcher and run the reaction overnight. Higher concentrations (>=10 μM of both Tag and Catcher) should go to completion in 30min-1hr. When performing coupling reactions for more than a few hours, I'd recommend you perform them at 4C. Loading 10 μL of 1-2 μM of your protein should allow you to see the band shift on an SDS-PAGE gel with Coomassie stain.
In my experience, temperature and pH are important factors when performing coupling. pH > 8.0 tends to reduce the rate of reaction significantly, as does pushing the temperature upwards of 37C (the protein prefers 25C and pH = 6.0). Most of the reactions I perform in the lab are at 4C overnight at pH = 7.4 between SpyCatcher003 and SpyTag1, and coupling is nearly complete. However, others in our lab have worked extensively with SpyCatcher002 and SpyTag1 reactions, which also tend to go to completion under the right conditions. Moreover, sometimes the protein that the SpyTag is fused to will alter the kinetics of the reaction, and short linkers to SpyTag may reduce your coupling efficiency.
While others are certainly more qualified to answer this question, hopefully this gives you enough information to work with!