I have used multiple imputations on 2 variables, say a and b.

Specifically, for some simplified model, there is no inclusion of a and b in that model.

I tried for 2 estimate with and without mi estimate and found that there is minimal difference in the 2 estimates which are shown below:

Code:
Multiple-imputation estimates
Conditional (fixed-effects) logistic regression

                                                Imputations       =          5
                                                Number of obs     =     29,292
                                                Average RVI       =     0.0000
                                                Largest FMI       =     0.0000
DF adjustment:   Large sample                   DF:     min       =   3.37e+59
                                                        avg       =   3.37e+59
                                                        max       =          .
Model F test:       Equal FMI                   F(  11, 5.8e+60)  =     113.38
Within VCE type:       Robust                   Prob > F          =     0.0000

                             (Within VCE adjusted for 549 clusters in UniqueID)
-------------------------------------------------------------------------------
     Response |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
  d_Softdrink |  -2.623978   .2845676    -9.22   0.000     -3.18172   -2.066236
    d_Juice25 |  -1.231593   .1890147    -6.52   0.000    -1.602055    -.861131
   d_FlavMilk |   .4261079   .2758369     1.54   0.122    -.1145225    .9667383
   d_Juice100 |    .058627   .2359539     0.25   0.804    -.4038341     .521088
 d_LowFatMilk |  -.7098718   .2183783    -3.25   0.001    -1.137885   -.2818582
  p_Softdrink |  -.8919193   .1083205    -8.23   0.000    -1.104223   -.6796151
    p_Juice25 |  -.7150817   .0572729   -12.49   0.000    -.8273345    -.602829
   p_FlavMilk |  -.9742113   .0732781   -13.29   0.000    -1.117834   -.8305888
p_BottleWater |  -.3403531   .0318025   -10.70   0.000    -.4026847   -.2780214
   p_Juice100 |  -.7869841   .0553303   -14.22   0.000    -.8954296   -.6785386
 p_LowFatMilk |   -.631621   .0536054   -11.78   0.000    -.7366856   -.5265565
-------------------------------------------------------------------------------
Code:
Iteration 0:   log pseudolikelihood = -13386.653  
Iteration 1:   log pseudolikelihood = -13164.407  
Iteration 2:   log pseudolikelihood = -13163.939  
Iteration 3:   log pseudolikelihood = -13163.939  

Conditional (fixed-effects) logistic regression

                                                Number of obs     =     56,682
                                                Wald chi2(11)     =     796.80
                                                Prob > chi2       =     0.0000
Log pseudolikelihood = -13163.939               Pseudo R2         =     0.2223

                              (Std. Err. adjusted for 549 clusters in UniqueID)
-------------------------------------------------------------------------------
              |               Robust
     Response |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
  d_Softdrink |  -2.831667   .3159078    -8.96   0.000    -3.450835   -2.212499
    d_Juice25 |  -1.307012   .2572536    -5.08   0.000    -1.811219   -.8028038
   d_FlavMilk |   .4484063   .3388518     1.32   0.186     -.215731    1.112543
   d_Juice100 |  -.2139086   .3353719    -0.64   0.524    -.8712255    .4434084
 d_LowFatMilk |   -.971099   .2941376    -3.30   0.001    -1.547598   -.3945998
  p_Softdrink |  -.8375092   .0893627    -9.37   0.000    -1.012657   -.6623616
    p_Juice25 |  -.6484222   .0764521    -8.48   0.000    -.7982655   -.4985789
   p_FlavMilk |  -.9374873   .0865078   -10.84   0.000    -1.107039   -.7679352
p_BottleWater |  -.3049194   .0426047    -7.16   0.000    -.3884231   -.2214156
   p_Juice100 |  -.6535157   .0789469    -8.28   0.000    -.8082488   -.4987827
 p_LowFatMilk |  -.5586918   .0708329    -7.89   0.000    -.6975217   -.4198619
-------------------------------------------------------------------------------
Is it true that mi estimate should be used only when I run analysis which includes a and/or b? Should I just need to estimate with estimation commands such as clogit, clogithet, logit, etc. without having mi estimate: clogit ... for estimation excluding a and b? The reason why I am confused is that after multiple imputation, I see datasets were imputed for all variables, not just a and b, but it keeps the missing proportion unchanged for the ones as in the original dataset.

Thanks!