significance of random effect in mgcv gam

Question. Am I correct that p = .126 above can be taken as the

Dear R-helpers,

I would like to test whether a random effect is significant when
implemented with bs="re" in mgcv gam. For example, if I run:

M3b <- gam(DVY  ~ s(SessIDX, fTX, bs = "re") + factor(TX),
            data = PCP,
            family = quasipoisson(link="log"), method="REML")
summary(M3b,all.p=TRUE)
gam.vcomp(M3b)

I obtain the the following output:

 > summary(M3b,all.p=TRUE)

Family: quasipoisson
Link function: log

Formula:
DVY ~ s(SessIDX, fTX, bs = "re") + factor(TX)

Parametric coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)   1.3282     0.2244   5.920 2.74e-07 ***
factor(TX)1  -1.0546     0.7210  -1.463     0.15
---
Signif. codes:  0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1

Approximate significance of smooth terms:
                  edf Ref.df     F p-value
s(SessIDX,fTX) 1.052      2 1.138   0.126

R-sq.(adj) =  0.388   Deviance explained = 39.5%
REML score =  37.67  Scale est. = 1.4172    n = 54

 > gam.vcomp(M3b)

Standard deviations and 0.95 confidence intervals:

                   std.dev      lower     upper
s(SessIDX,fTX) 0.07842742 0.01095655 0.5613865
scale          1.19029872 0.97816911 1.4484316

Rank: 2/2

Question. Am I correct that p = .126 above can be taken as the p-value
associated with the random effect?

Thanks.

Will Shadish